Coaxial pumping apparatus with internal power fluid column

ABSTRACT

The present application relates generally to pumps, and more particularly to piston type pumps having increased energy efficiency, systems incorporating such piston type pumps, and methods of operating piston type pumps.

INCORPORATION BY REFERENCE TO RELATED APPLICATIONS

Any and all priority claims identified in the Application Data Sheet, orany correction thereto, are hereby incorporated by reference under 37CFR 1.57. This application is a continuation of U.S. application Ser.No. 13/837,326, filed Mar. 15, 2013, which is a continuation-in-part ofU.S. application Ser. No. 12/023,016, filed Jan. 30, 2008, now U.S. Pat.No. 8,454,325, which claims the benefit under 35 U.S.C. §119(e) of U.S.Provisional Application No. 60/898,377, filed Jan. 30, 2007. U.S.application Ser. No. 13/837,326 is a continuation-in-part of U.S.application Ser. No. 13/169,243, filed Jun. 27, 2011, now U.S. Pat. No.8,535,017, which is a continuation of U.S. application Ser. No.10/587,903, now U.S. Pat. No. 7,967,578, which is the national phaseunder 35 U.S.C. §371 of PCT International Application No.PCT/CA05/00096, filed Jan. 27, 2005, which is a continuation-in-part ofU.S. application Ser. No. 10/765,979, filed on Jan. 29, 2004, nowabandoned. Each of the aforementioned applications is incorporated byreference herein in its entirety, and each is hereby expressly made apart of this specification.

FIELD OF THE INVENTION

The present application relates generally to pumps, and moreparticularly to piston type pumps having increased energy efficiency,systems incorporating such piston type pumps, and methods of operatingpiston type pumps.

BACKGROUND OF THE INVENTION

It has been estimated that approximately 85% of the total cost ofoperating a conventional pump is attributable to energy consumption.Pumping systems account for nearly 20% of the world's electrical energydemand and range from 25% to 50% of the energy required by industrialplant operations.

Similarly, maintenance costs account for approximately 10% of the totalcost of operating a conventional pump.

Pumping liquids against substantial hydraulic heads is a problemencountered in pumping out mines, deep wells, and similar applicationssuch as pumping water back up, over a hydro dam during low energy usageperiods, for subsequent recovery during high energy usage periods, andfor run-of-the-river hydro power applications utilizing the potentialenergy of water in a standing column.

Several earlier patents attempt to provide devices which utilize apiston type pump where energy is recovered from a column of liquidacting downwardly on the piston, as the piston moves downwardly, toassist in subsequently raising the piston with a volume of liquid to bepumped upwardly. An example of such an earlier patent is U.S. Pat. No.6,193,476 to Sweeney. However such earlier devices have not beenefficient enough to justify commercial usage. In the Sweeney patent, forexample, the efficiency of the apparatus is significantly reduced due tothe upper piston 38 having the same cross-sectional area as lower piston43. Thus the pressure of liquid acting upwardly on the lower piston 43inhibits downward movement of the upper piston 38 under the weight ofthe liquid in the cylinder above.

SUMMARY OF THE INVENTION

It is an object to the invention to provide an improved pumpingapparatus capable of pumping liquids against significant hydraulicheads, such as encountered in deep wells or in pumping out mines,without requiring pumps with high output heads.

It is a further object of the invention to provide an improved pistontype pumping apparatus with provision for energy recovery or energyconservation, having significantly improved efficiency compared withprior art devices.

It is still further object of the invention to provide an improvedpiston type pumping apparatus which is simple and rugged inconstruction, and efficient to operate and install.

BRIEF DESCRIPTION OF THE DRAWINGS

Features of the present disclosure will become more fully apparent fromthe following description and appended claims, taken in conjunction withthe accompanying drawings. It will be understood these drawings depictonly certain embodiments in accordance with the disclosure and,therefore, are not to be considered limiting of its scope; thedisclosure will be described with additional specificity and detailthrough use of the accompanying drawings. An apparatus, system or methodaccording to some of the described embodiments can have several aspects,no single one of which necessarily is solely responsible for thedesirable attributes of the apparatus, system or method. Afterconsidering this discussion, and particularly after reading the sectionentitled “Detailed Description of the Preferred Embodiment” one willunderstand how illustrated features serve to explain certain principlesof the present disclosure.

FIG. 1 provides a cross-sectional view of a vertically oriented pumpincluding a pump housing, an inlet near the bottom of the pump, and anoutlet near the top of the pump.

FIG. 2 provides a cross-sectional view of a pump having a tapered pumpinlet.

FIG. 3 provides a cross-sectional view of a pump wherein the power fluidacts on the bottom of the rod portion of the transfer piston.

FIG. 4A provides a cross-sectional view of a pump during the productionstroke.

FIG. 4B provides a cross-sectional view of a pump during the recoverystroke.

FIG. 5A provides a cross-sectional view of a pump wherein an oscillatingpressure is provided by a piston and cylinder system.

FIG. 5B provides a cross-sectional view of a pump wherein an oscillatingpressure is provided by alternating the conduit valve and power releasevalve.

FIG. 6A provides a cross-sectional view of a pump fitted with a filteror screen to reduce the risk of plugging within the pump. The pump isdepicted during the power stroke.

FIG. 6B provides a cross-sectional view of a pump according to preferredembodiment. The pump is depicted during the recovery stroke.

FIG. 6C provides a cross-sectional view of a pump according to apreferred embodiment. The pump is depicted during a cleaning operationwherein the transfer piston is lifted beyond its highest point duringnormal operation.

FIG. 7A provides a cross-sectional view of a pump coaxial disconnect ina closed position.

FIG. 7B provides a cross-sectional view of a pump coaxial disconnect inan open position.

FIG. 8A provides a cross-sectional view of a subterranean switch pumpduring a power stroke.

FIG. 8B provides a cross-sectional view of a subterranean switch pumpduring a pump recovery stroke.

FIG. 9 provides a cross-section view of one embodiment of a downholepump.

FIG. 9A provides a cross-section view of one embodiment of a 3.5″downhole pump.

FIG. 9B provides a cross-section view of a connection location for thepower fluid tube and the product fluid coaxial tube.

FIG. 9C provides a cross-section view of the embodiment of FIG. 9Aincluding the main piston seal.

FIG. 9D provides a cross-section view of the embodiment of FIG. 9Aincluding the seal between a power fluid chamber and a transfer chamber.

FIG. 9E provides a cross-section view of the embodiment of FIG. 9Aincluding the intake valve located within the bottom of the pump.

FIG. 10 provides another embodiment of a downhole pump.

FIG. 10A provides a cross-sectional view of a 1.5″ stacked downholepump.

FIG. 10B provides a cross-sectional view of the embodiment of FIG. 10Aincluding the power fluid and product fluid coaxial tubes.

FIG. 10C provides a cross-sectional view of the embodiment of FIG. 10Aincluding a main piston seal.

FIG. 10D provides a cross-sectional view of the embodiment of FIG. 10Aincluding a bottom piston seal.

FIG. 11 provides another embodiment of a downhole pump.

FIG. 12 provides a figure illustrating an efficiency comparison betweena conventional electric pump and a pump of a preferred embodiment.

FIG. 13 provides a graph illustrating efficiency of various pumps basedupon a ratio of two areas on a piston.

FIG. 14 is a simplified elevational view, partly in section, of apumping apparatus according to an embodiment of the invention;

FIG. 15 is a simplified elevational view, partly in section, of theupper fragment of an alternative embodiment employing a centrifugalpump;

FIG. 16 is a graph of the efficiency of the pressure head concept of thepump;

FIG. 17 is a sectional view of the embodiment of FIG. 14 showing theForce Balance in the pump;

FIGS. 18A and 18B are simplified sectional views showing Pressure HeadConcept of a pump and the Power Cylinder Concept of the pump.

FIGS. 19A and 19B are simplified elevational views, partly in section,of a pumping apparatus in a power stroke and a recovery strokerespectively according to another embodiment of the invention.

FIG. 20 shows a schematic of a system wherein water at a higher level isdirected straight to the pump to power the pump stroke.

FIG. 21 depicts an embodiment of the Hygr Fluid System wherein thehydraulic cylinder on the surface moves forward and produces a hydraulicimpulse transmitted through the delivery pipe to the pump.

FIG. 22 is a photograph showing two hydraulic accumulators and waterpumped from downhole.

FIG. 23 is a photograph showing a drive unit (forward box) and controlunit (rear box).

FIG. 24A depicts wells in close proximity controlled by one drive unit.

FIG. 24B depicts a drive unit for controlling wells as in FIG. 23.

FIG. 25 depicts a system utilizing an accumulator with a Hygr FluidSystem pump.

FIG. 26 depicts a system utilizing an accumulator drive and recyclesystem with a Hygr Fluid System pump.

FIG. 27 depicts a Blair Drive system providing oil to a Hygr FluidSystem.

FIG. 28 depicts a Blair Drive system wherein gas freeflows up thecasing, energizing the Blair Piston and oil pump.

FIG. 29 is a block diagram depicting the 4G system.

FIG. 30 is a block diagram depicting the power stroke of the 4G system.

FIG. 31 is a block diagram depicting the recharge stroke 4G system.

FIG. 32 depicts a system utilizing an accumulator drive with a dischargereset.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the following detailed description, only certain exemplaryembodiments have been shown and described, simply by way ofillustration. As those skilled in the art would realize, the describedembodiments may be modified in various different ways, all withoutdeparting from the spirit or scope of the present disclosure.Accordingly, the drawings and description are to be regarded asillustrative in nature and not restrictive. In addition, when an elementis referred to as being “on” another element, it can be directly on theanother element or be indirectly on the another element with one or moreintervening elements interposed therebetween. Also, when an element isreferred to as being “connected to” another element, it can be directlyconnected to the another element or be indirectly connected to theanother element with one or more intervening elements interposedtherebetween. Hereinafter, embodiments of the disclosure will bedescribed with reference to the attached drawings. If there is noparticular definition or mention, terms that indicate directions used todescribe the disclosure are based on the state shown in the drawings.Further, the same reference numerals indicate the same members in theembodiments.

FIG. 1 illustrates an embodiment of a pumping apparatus of a preferredembodiment. The vertically oriented pump 100 preferably includes a pumphousing 102, at least one inlet 104 near the bottom of the pump 100, andat least one outlet 106 near the top of the pump 100. The pump inlet 104includes a valve 108. The valve 108 is preferably a one-way valve,allowing fluid to flow through the inlet 104 into a transfer chamber 110inside the pump 100, but not in the reverse direction. More preferably,the inlet valve 108 is a self-actuating valve, such that it requires noelectronic or manual control, but rather opens and closes solely by theforce of the fluid moving therethrough and/or by pressure changes in thetransfer chamber 110. In such embodiments, any suitable type of one-wayvalve can be utilized, including check valves and the like.

Check valves are valves that permit fluid to flow in only one direction.Ball check valves contain a ball that sits freely above a seat, whichhas only one opening therethrough. The ball has a diameter that islarger than the diameter of the opening. When the pressure behind theseat exceeds the pressure above the ball, liquid is allowed to flowthrough the valve; however, once the pressure above the ball exceeds thepressure below the seat, the ball returns to rest in the seat, forming aseal that prevents backflow. The ball can also be connected to a springor other alignment device. Such alignment devices are useful if the pumpoperates in a non-vertical orientation. In some embodiments, the ballcan be replaced by another shape, such as a cone.

Swing check valves can also be utilized. Swing check valves use a hingeddisc that swings open with the flow. Any other suitable type of checkvalve, including dual flap check valves and lift check valves, can alsobe utilized. Numerous other types of valves can be utilized, includingreed valves, diaphragm valves. The valves can optionally beelectronically controlled. Using standard computer process controltechniques, such as those known in the art, the opening and closing ofeach valve can be automated. In such embodiments, two-way valves canadvantageously be utilized.

Any suitable number of inlets and outlets can be employed, for example,1, 2, 3, 4, 5, or more inlets, and 1, 2, 3, 4, 5, or more outlets.Preferably three (3) inlets and three (3) outlets are employed.

The pump can be of any suitable size. The preferred size can be selectedbased upon various factors such as the amount of liquid to be pumped,the type of liquid, and other factors. For example, the pump housing canhave a diameter of 1, 3, 6, 12, 24, or 36 inches or more. In a preferredembodiment, the pump housing 102 has an outer diameter of about 3.5inches. In another preferred embodiment, the pump housing 102 has anouter diameter of about 1.5 inches.

The pump 100 also includes a transfer piston 120, which isreciprocatingly mounted therein. The transfer piston 120 typicallyincludes a piston portion 122 and a rod portion 124. The piston portion122 includes a channel 125 and a valve 126, which is referred to hereinas the “transfer piston valve.” Preferably, the transfer piston valve126 is a one-way valve, allowing fluid to flow from the transfer chamber110 into a product cylinder 130, but not in the reverse direction fromthe product cylinder 130 to the transfer chamber 110.

The pump 100 also includes a vertically oriented power fluid column 140,which defines a power fluid tube 142. The power fluid column can beoriented in any suitable manner, and is not limited to a verticalorientation. For example, the power fluid column can be horizontal, orat any angle displaced from the vertical. In addition, the pump 100 canoperate at any angle, including vertical, horizontal, or any angletherebetween. The power fluid tube comprises an inlet 144 such thatpower fluid can be provided to and/or removed from the power fluid tube142.

The power fluid column 140 further includes at least one passageway 146.In preferred embodiments, the power fluid column includes 1, 2, 3, 4, 5,6 or more passageways. This passageway 146 allows power fluid to flowfreely between the power fluid tube 142 and a power fluid chamber 150.Preferably, the passageway 146 is located near the bottom of the powerfluid tube 142.

In the embodiment illustrated in FIG. 1, the power fluid chamber 150 isdefined by the exterior surface of the power fluid column 140 and thetransfer piston 120. The power fluid chamber 150 has a top 152, alsoreferred to herein as the “inner surface area.” In the embodimentillustrated in FIG. 1, the inner surface area 152 is a portion of thebottom of the piston portion 122 of the transfer piston 120. The innersurface area 152 is the surface area upon which the power fluid acts.The passageway 146 through which the power fluid enters the power fluidchamber 150 is located below the inner surface area 152.

To enclose the power fluid chamber 150, the rod portion 124 of thetransfer piston 130 extends coaxially about the power fluid column 140.The shape of the power fluid column 140 and the transfer piston 120 arechosen such that they form a slideable seal both at the top and thebottom of the power fluid chamber 150. For example, in the embodimentillustrated in FIG. 1, the power fluid column 140 increases in diameterto form a slidingly sealable engagement with the rod portion 124 of thetransfer piston 120 at the bottom of the power fluid chamber 150,thereby ensuring a secure power fluid chamber 150. The spacing betweencomponents, such as between the power fluid column 140 and the rodportion 124, is typically determined by the seal utilized. The type ofseal utilized is determined by the operating conditions (i.e. pressureand temperature) and the fluids utilized. In a preferred embodiment, astandard o-ring seal is utilized. In high temperature applications, aring such as those used in automobile pistons can be utilized.

FIG. 1 is a simplified drawing of a pump of one preferred embodiment.Seals and other conventional elements are omitted from the drawing forpurposes of illustration. Numerous modifications can be made to theembodiment illustrated in FIG. 1. As just one example, the pistonportion 122 of the transfer piston 120 can alternatively be located atthe bottom of the rod portion 124, rather than adjacent the top asillustrated in FIG. 1. In addition, the rod 124 and piston portions 122can vary in shape and thickness. For example, the thickness of thepiston portion 122 can be selected based on the pressure applied.

The operation of the pump illustrated in FIG. 1 is described inconnection with pumping of oil from an oil well. However, the pumps ofpreferred embodiments are also suitable for pumping other liquids aswell (e.g., ground water, subterranean liquids, brackish water, seawater, waste water, cooling water, gas, coolants, and the like).

The operating cycle of the pump 100 can be divided into two separatestages, referred to as the “production stroke” or “power stroke” and the“recovery stroke.” During the production stroke, water is supplied underpressure through the power fluid inlet 144. This forces water down thepower fluid tube 142, through the passageway 146, and into the powerfluid chamber 150. The water acts on the inner surface area 152 to liftthe transfer piston 120. As the transfer piston 120 lifts against theweight of the oil in the product cylinder 130, the transfer piston valve126 closes. As the transfer piston 120 is lifted, the oil in the productcylinder 130 is forced out through the pump outlet 106. This oil canthen be recovered by suitable means or apparatus, such as known in theart. For example, the outlet 106 can be connected to a pipe, whichdirects the oil to a desired location. Sometimes, the oil can bedelivered to the wellhead, where the oil can be directed to separationand/or storage facilities. Storage facilities, when employed, can beeither above ground or below ground. Where crude oil is recovered, theoil can be transferred to a refinery or refineries by pipeline, ship,barge, truck, or railroad. Where natural gas is recovered, the gas istypically transported to processing facilities by pipeline. Gasprocessing facilities are typically located nearby so impurities such assulfur can be removed when possible. In cold climate applications, theoil can be transferred via heated lines.

As the transfer piston 120 is rising with the transfer piston valve 126closed as described above, a vacuum, partial vacuum, or low pressurevolume is created in the transfer chamber 110. The decrease in pressurein the transfer chamber 110 causes the inlet valve 108 to open and oilfrom the well is drawn into the transfer chamber 110 through the pumpinlet 104.

The transfer piston 120 rises until the top of the transfer piston 120contacts the top of the pump or, alternatively, until the forcegenerated by the power fluid and acting on the inner surface area 152equals the force generated by the weight of the oil in the productcylinder 130 plus the weight of the transfer piston 120. As the transferpiston 120 reaches the highest point (similar to top dead center for apiston in an engine), the product cylinder 130 is at its smallest volumeand the transfer chamber 110 is at its largest volume. The inlet valve108 is open, but the transfer piston valve 126 is closed.

As the transfer piston 120 reaches its highest point, the pressure ofthe power fluid is reduced until the downward force, provided by gravityacting on the weight of the oil in the product cylinder 130, the weightof the oil in the product pipeline above the pump, and the weight of thetransfer piston, is greater than the upward force provided by the powerfluid acting on the inner surface area. This causes the transfer piston120 to fall, and initiates the recovery stroke. In some embodiments, thepressure of the power fluid can be reduced such that the power fluidchamber serves as a vacuum or partial vacuum, providing an additionalforce to lower the transfer piston 120. In some embodiments, the fluidin the product cylinder can be pumped to a higher elevation or into apressure vessel to supply additional energy for the recovery stroke.

As the transfer piston 120 lowers, the pressure inside the transferchamber 110 increases. The increase in pressure causes the inlet valve108 to close, thereby sealing the pump inlet 104. Alternatively, sensorscan be employed and the valves controlled electronically. As thepressure inside the transfer chamber 110 continues to increase due tothe lowering transfer piston 120, the transfer piston valve 126 opens,thereby allowing oil located within the transfer chamber 110 to flowinto the product cylinder 130. The transfer piston 120 continues tolower until the rod portion 124 of the transfer piston 120 contacts thebottom of the pump 100, or alternatively until the force generated bythe power fluid equals the force generated by the weight of the oil andthe weight of the transfer piston. Thereafter, power fluid is introducedunder pressure, acting on the inner surface area 152 and initiating theproduction stroke.

The operation of the pump is maintained by providing an oscillating orperiodic pressure to the power fluid. The power fluid can be anysuitable fluid. In one embodiment, the power fluid is water; however,numerous other power fluids can be utilized, including but not limitedto sea water, waste water from oil recovery processes, and product fluid(i.e. oil if the pump is being used in oil recovery processes). In otherembodiments, the power fluid can be gas or steam. Thus, the term“fluid,” as used herein, is not restricted to liquids, but is intendedto have a broad meaning, including gases and vapors. In one embodiment,the power fluid is air. In another embodiment, the power fluid is steam.

The appropriate power fluid for a particular application can be based ona variety of factors, including cost and availability, corrosiveness,viscosity, density, and operating conditions. For example, the powerfluid can be the same fluid as the product fluid. This allows theproduct fluid and the power fluid to have the same density, therebysimplifying the forces acting on the transfer piston. Alternatively, amore dense power fluid can be utilized. Utilizing a power fluid that ismore dense than the product fluid allows the pump to operate with either(a) the power fluid supplied at a lower pressure, or (b) a smaller innersurface area. For example, in some embodiments, brine or mercury can beutilized. Preferably, a low-viscosity power fluid is utilized, as use ofa high viscosity power fluid may cause pressure loss due to frictionbetween the power fluid and the power fluid column.

In some embodiments, such as where the pump is utilized in hightemperature applications, a power fluid such as motor oil can beutilized. Similarly, various oils and liquids with low freezing pointscan be utilized in cold environments.

The pump can be operated by one power source, or a number of pumps canbe operated by the same power source. For example, in some applicationssuch as construction, mine dewatering, or other commercial andindustrial applications, several pumps can be operated by the same powersource. In addition, several pumps can be operated using an air system,such as in a manufacturing facility.

The pump 100 and its components can be any suitable shape. The use ofthe terms column, chamber, tube, rod, and the like are not intended tolimit the shape of the components. Rather, these terms are used solelyto aid in describing particular embodiments. For example, with referenceto FIG. 1, the pump housing 102 and power fluid column 140 can both besubstantially cylindrical in shape. Thus, the piston portion 122 of thetransfer piston 120 seals the annular gap between these two cylinders.However, the pumps of preferred embodiments are not limited to thisconfiguration; the pump housing 102 can be any shape, and the powerfluid column 140 can be any shape. For example, besides being formed ina circular shape, the pump components can also be square, rectangular,triangular, or elliptical.

The pump housing 102 and the pump components, such as the power fluidcolumn 140 and the transfer piston 120, can be constructed of anysuitable material. For example, in preferred embodiments, thesecomponents can be constructed of 304 or 316 stainless steel. In someembodiments, such as when the pump is in contact with highly corrosivematerials, a 400 series stainless steel can be used. One of skill in theart will appreciate that selection of the pump materials depends on avariety of factors, including strength, corrosion resistance, and cost.In high temperature applications, pump components can preferably beconstructed of ceramic, carbon fiber, or other heat resistant materials.

Referring still to FIG. 1, the upper surface of the transfer piston 120defines an area A₁. This upper surface can be planar, but can also beconcave, convex, or linearly sloping. The surface area A₁ supports theweight of the fluid in the product cylinder 130 and any standing columnof fluid above the pump. That is, the fluid in the product cylinder 130and in any vertical pump outlet pipes creates a downward force on thetransfer piston 120. This downward force is equal to the mass of theproduct fluid multiplied by gravity, or alternatively, it is equal tothe pressure of the product fluid in the product cylinder 130 multipliedby the surface area A₁. Gravity acting on the weight of the transferpiston 120 also creates a downwards force.

The bottom surface of the transfer piston 120 exposed to the fluid inthe transfer chamber 110 also defines an area, A₂. A₂ is the surfacearea upon which the fluid in the transfer chamber acts. During therecovery stroke, the fluid in the transfer chamber 110 exerts an upwardsforce on the transfer piston equal to the pressure inside the transferchamber 110 multiplied by the surface area A₂ upon which it acts. Forthe embodiment illustrated in FIG. 1, the difference between A₁ and A₂represents the inner surface area, A₃, the area upon which the pressurefluid acts.

Therefore, if:

-   -   P₁=Pressure of product fluid in the product chamber 130    -   A₁=Area upon which fluid in the product chamber 130 acts    -   P₂=Pressure of fluid in the transfer chamber 110    -   A₂=Area upon which fluid in the transfer chamber 110 acts    -   P_(pf)=Pressure of power fluid in the power fluid chamber 150    -   A₃=(A₁−A₂)=Pressure upon which power fluid acts (“inner surface        area”)    -   T=Weight of the transfer piston

And ignoring any forces caused due to friction between the componentsand seals inside the pump, then:

Force_(down) =P ₁ A ₁ +T

Force_(up) =P ₂ A ₂ +P _(pf) A ₃

Accordingly, changes to the values for A₁ and A₂ influence the amount ofpressure required for the power fluid to lift the piston during thepower stroke. The work required to lift the piston is determined bymultiplying the force exerted by the power fluid by the distance thepiston travels. Therefore, if S represents the distance the pistontravels from its lowest position to its highest position, then the work(W_(in)) necessary to lift the piston is:

W _(in) =P _(pf) A ₃ S

Accordingly, the amount of work required is also impacted by the ratioof A₁:A₃, as is the pump's efficiency. In a preferred embodiment, theratio of A₁:A₃ is from about 1.25 to about 4.

FIG. 2 illustrates another embodiment of a pump. The pump is, in manyrespects, similar to the embodiment described above in connection withFIG. 1. As shown in FIG. 2, the pump inlet 204 is not located on thebottom of the pump 100, as illustrated in FIG. 1. The inlet 204 can belocated at any point below the transfer piston valve 226. In a preferredembodiment, the inlet 204 is not located on the bottom of the pumphousing 202, because when the pump is placed down a well, the bottom ofthe pump can rest on the ground beneath the fluid being pumped. Pumpinlets on the bottom of the pump often become plugged. As illustrated inFIG. 2, the pump inlet 204 can be tapered such that the narrowestportion of the inlet is at the exterior of the pump housing 202. In apreferred embodiment, the inlet has a one-eighth inch external opening,and has an inwardly enlarging taper. This tapering of the inlet 204prevents suspended particles from becoming lodged within the pump.

The embodiment illustrated in FIG. 2 provides one example of a one-wayvalve system that can be utilized. The inlet 204 comprises a hole orpassageway, as illustrated. A conical check valve member 208 is locatednear the bottom of the power fluid column 240. As the pressure insidethe transfer chamber 210 decreases, the check valve opens, allowingfluid to flow through the inlet 204 into the transfer chamber 210. Theconical valve member 208 can rise up freely, or it can rise until itreaches a stop 209, as illustrated in FIG. 2. The valve member 208 canalso be slideably coupled to the power fluid column 240.

As illustrated, the pump 200 is in the recovery stroke. The increasedpressure inside the transfer chamber 210 has caused the inlet valvemember 208 to lower. As illustrated, the valve member 208 has loweredand formed a sealing engagement with the interior surface of the pumphousing 202 (often referred to as the valve “seat”), thereby preventingfluid from flowing out of the transfer chamber 210 through the inletholes 204.

The embodiment illustrated in FIG. 2 also utilizes a conical check valveas the transfer piston valve 226. Any suitable type of one-way valve canbe used, and any combination of valve types can be used for the pumpinlet valve 208 and the transfer piston valve 226. As previouslydescribed, automated valves and two-way valves can also be utilized withappropriate controls. As described previously in connection with pumpinlet valve 208, the conical portion of the transfer piston valve 226can be slideably coupled to the power fluid column 240. The amount oftravel the conical portion of the piston valve 226 has can be limited bya stop (not shown). In a preferred embodiment, the valves 208, 226 arespring loaded. In other embodiments, the valves can be guided by othermechanisms, or, alternatively, free of constraints.

In the embodiment illustrated in FIG. 2, the transfer piston 220comprises a channel 225. The transfer piston channel 225 can also betapered to prevent solid particles from being lodged therein. Any numberof piston channels and valves can be utilized. For example, the transferpiston can include 1, 2, 3, 4, 5, or 6 or more channels and/or valves.

As illustrated, the pumping apparatus 200 is in the recovery stroke. Thepressure inside the transfer chamber 210 is greater than the pressureinside the product cylinder 230, and the transfer piston valve 226 isopen, allowing fluid to flow from the transfer chamber 210 into theproduct cylinder 230.

The embodiment illustrated in FIG. 2 employs a preferred method forsealing the transfer piston 220. Sealing mechanisms 228 are used toprevent fluid communication between the transfer chamber 210 and theproduct cylinder 230, and between the transfer piston 220 and the powerfluid column 240 to ensure a secure power fluid chamber 250. Methods ofcreating and maintaining a seal are well known in the art, and any suchsuitable method of forming a seal can be utilized with the pumpsprovided herein. For example, rings formed of polyurethane orpolytetrafluoroethylene (PTFE) can be used.

The embodiment illustrated in FIG. 2 further utilizes a top cap 260. Thetop cap 260 serves as a mechanism 264 for connecting the source of thepower fluid to the power fluid tube 242. Any suitable connectionmechanism, including those connection mechanisms as known in the art,can be employed. The top cap 260 also provides a mechanism 262 forconnecting the pump outlet 206 to a recovery unit (not shown). Forexample, the top cap 260 can include threads to which a pump can beconnected, or a seat to which a flanged pipe can be connected.

FIG. 3 illustrates another embodiment of a pumping apparatus. Theembodiment illustrated in FIG. 3 is similar in many respects to theembodiments illustrated in FIG. 1 and FIG. 2. However, the embodiment inFIG. 3 utilizes the bottom of the rod portion 324 of the transfer piston320 as the inner surface area 352 upon which the power fluid acts.Accordingly, the power fluid chamber 350 is enclosed not only by the rodportion 324 of the transfer piston 320 and the power fluid column 340,but also by a third component, referred to herein as the power fluidcontainment portion 356. This containment portion 356, which provides anouter wall for the power fluid chamber 350, can be formed by increasingthe thickness of the pump housing 302 below the inlet 304, asillustrated in FIG. 3. However, numerous other configurations and/ormechanisms can alternatively enclose the power fluid chamber. As anexample, if the pump 300 has a 3 inch diameter, and the power fluidcolumn 340 and power fluid chamber 350 have a combined diameter of 1.5inches, then the pump housing 302 below the inlet 304 can be 1.5 inchesthick. However, if the embodiment illustrated in FIG. 1 is utilized, andthe transfer chamber occupies an additional 1 inch of the diameter, thenthe pump housing 302 can be only 0.5 inches thick.

The transfer piston 320, which is reciprocatingly mounted about thepower fluid column 340, forms a slideable and sealing engagement withboth the power fluid column 340 and the power fluid containment portion356. The pump inlet 304, as illustrated in the embodiment in FIG. 3, islocated above the power fluid containment portion 356 and the uppersurface of the power fluid containment portion 356 serves as the basefor the transfer chamber 310. However, the inlet 304 can alternativelyextend through the power fluid containment portion 356.

FIG. 4A and FIG. 4B illustrate another embodiment of the pumpingapparatus. In many ways, the embodiment illustrated in FIG. 4A and FIG.4B is similar to the embodiment discussed above in connection with FIG.3. FIG. 4A and FIG. 4B illustrate using conical check valves for boththe inlet valve 408 and the transfer piston valve 426.

The embodiments illustrated in FIG. 3, FIG. 4A, and FIG. 4B operate inmanner similar to those illustrated in FIG. 1 and FIG. 2. The operationof the pumps of embodiments illustrated in FIG. 4A and FIG. 4B is asfollows. Pump dimensions and characteristics described herein areprovided to aid in the description only, and are not meant to limit thescope of the application.

FIG. 4A represents one embodiment of a pump during the productionstroke. The pump 400 can have any outer diameter, including 1, 1.5, 2,3, 4, 6, 12, or 24 inches or more. The pump 400 can be any height. In apreferred embodiment, the outer diameter of the pump housing 402 isabout 1.5 inches, and the power fluid column 440 is about 0.5 inches indiameter. The pump 400, measured from the bottom of the pump to the topof the top cap 460, is about 19 inches in height. The center of theinlet hole 404 is about 8 inches from the bottom of the pump. When thetransfer piston 420 is at its lowest position, the height of thetransfer chamber 410 is about 0.7 inches. The pump is placed in a wellat a depth of about 1000 feet and both the product fluid and the powerfluid are water.

The fluid in the product cylinder 430, and the standing column of waterabove the pump, exerts a pressure P₁ on the transfer piston 420. Thedownward force acting on the transfer piston 420 is equal to thispressure multiplied by the surface area of the piston upon which itacts, A₁. Gravity acting on the weight of the transfer piston 420 alsocreates a downwards force; however, because the piston of thisembodiment is only about 1 to about 2 pounds, its effect may benegligible. The resistance R caused by the friction of the seals alsoexerts a downward force as the piston 420 is raised.

The force lifting the transfer piston 420 is equal to the power fluidpressure, P_(pf), multiplied by the surface area upon which it acts, A₃.To lift the transfer piston, the force supplied by the power fluid mustbe greater than the downward force previously discussed. Therefore, thenet force on the piston is given by:

F _(net) =F _(up) −F _(down) =P _(pf) A3−P ₁ A ₁ −R

Although the resistance of the seals can be considered it is ignoredhere to describe this embodiment. In some embodiments, the ratio of A₁to A₃ is between about 1.25 and about 4. In a preferred embodiment, theratio of A₁:A₃ is about 2:1. Therefore,

Fnet=P _(pf) A ₃ −P ₁2A ₃

In order for this net force to be positive, the pressure of the powerfluid P_(pf) must be at least twice as great as the pressure of thestanding column, P₁. Since the pump is placed at a depth of about 1000ft, P₁ is approximately 445 psi (pounds per square inch). The powerfluid is supplied at least double this pressure, or 890 psi. Because theforce exerted by the power fluid is proportional to its density, it canbe seen that if a power fluid is utilized that is twice as dense as thewater being pumped, the power fluid only needs to be supplied at 445 psito raise the piston.

When power fluid is supplied at this pressure, the power fluid actsagainst the inner surface area 452, thereby causing the transfer piston420 to rise. As the transfer piston 420 lifts against the weight of thefluid in the product chamber 430, the transfer piston valve 426 closes,thereby sealing the transfer piston channel 425. As the transfer piston420 rises, the fluid in the product chamber 430 is forced out of thepump through the pump outlet 406.

As the transfer piston 420 rises with the transfer piston valve 426closed, the pressure in the transfer chamber 410 decreases. The pressuredrop inside the transfer chamber 410 causes the inlet valve 408 to open,thereby allowing fluid from the source to be drawn through the pumpinlet 404 into the transfer chamber 410. As described previously, theinlet holes can be tapered to prevent debris from becoming lodgedtherein. As illustrated, the inlet valve 408 can be guided by, oralternatively slideably coupled to, the rod portion 424 of the transferpiston 420. The transfer piston 420 rises until the top of the transferpiston 420 reaches a predetermined stopping point, such as when thetransfer piston hits the top cap 460, or alternatively until the forcegenerated by the power fluid equals the force generated by the weight ofthe product fluid and the weight of the transfer piston 420. For theembodiment described above, the top of the piston stroke can be set bydecreasing the pressure of the power fluid below 890 psi. When thetransfer piston is at the top of its stroke, the transfer chamber isabout 6.7 inches in height, resulting in a stroke length of about 6inches.

Once the transfer piston 420 reaches its highest point, the recoverystroke begins. As illustrated in FIG. 4B, during the recovery stroke thepressure of the power fluid is reduced until the weight of the fluid inthe product chamber 430 plus the weight of the transfer piston 420 isgreater than the force provided by the power fluid and the fluid in thetransfer chamber 410. This causes the transfer piston 420 to fall,thereby increasing the pressure of the trapped fluid in the transferchamber 410. The increased pressure inside the transfer chamber 410causes the inlet valve 408 to close and seal the pump inlet 404. As thepressure continues to increase inside the transfer chamber 410, itcauses the transfer piston valve 426 to open, and fluid is forced fromthe transfer chamber 410 to the product chamber 430 via the transferpiston channel 425. Like the pump inlet holes, the transfer pistonchannel 425 can be tapered to prevent debris from becoming lodgedtherein. In some embodiments, the transfer piston channel 425 had adiameter that is larger than the diameter of the pump inlet holes,thereby allowing any particles that enter the inlet 404 to pass throughthe pump 400. The transfer piston 420 continues to fall until the bottomof the rod portion 424 of the transfer piston 420 contacts the bottom ofthe pumping apparatus, or alternatively until the upwards forcegenerated by the power fluid and the fluid in the transfer chamber 410equals the downwards force generated by both the weight of the fluid inthe product chamber 430 and the weight of the transfer piston 420.

The speed at which the pump operates can be varied as desired. The timerequired for one “stroke,” which is defined as the transfer piston 420moving from its lowest position, through its highest position andreturning to its lowest position, can be set by the operator. For theembodiment described above, wherein the outer diameter of the pump isabout 1.5 inches, a preferred speed is about 6 strokes per minute, whichprovides a displaced volume of about three barrels per day. However, anyrange of speeds can be utilized depending upon the application. Forexample, in some embodiments, only one stroke per minute can bepreferable. In other applications, speeds of 20 strokes per minute ormore can be preferable. The volume of product fluid pumped is determinedby the speed of the pump and the length of the stroke. Any suitablestroke length can be utilized, including 6, 12, 24, or 36 inches ormore.

The operating cycle of the pump 400 is maintained by providing anoscillating pressure to the power fluid. This oscillating pressure canbe provided by any suitable method, including a number of methods knownin the art. Among such methods are those described below and thosedisclosed in United States Patent Publication No. 2005-0169776-A1, thecontents of which are incorporated herein by reference in its entirety.

For example, as illustrated in FIG. 5A, the oscillating pressure can beprovided by a piston and cylinder system, wherein the piston is moved bya motor or engine with a crank mechanism, or a pneumatic or hydraulicdevice. These systems can be controlled manually, by an electronictimer, by a programmable logic controller (“PLC”), by computer, or by apendulum. As illustrated in FIG. 5A, a conduit 546 delivers power fluidto the power fluid inlet 544 from a power fluid source 570. The powerfluid source 570 comprises a cylinder 572 and a power fluid piston 574.During the power stroke, the power fluid piston 574 moves to the left,forcing power fluid from the power fluid cylinder 572, through theconduit 546, to the power fluid inlet 544. This increases the powerfluid pressure inside the power fluid chamber 550, thereby lifting thetransfer piston 520. During the recovery stroke, the power fluid piston574 moves to the right. Power fluid is forced out of the power fluidchamber 550, and the transfer piston 520 lowers.

In some applications, the power fluid in the conduit 546 alone canprovide substantial pressure to the power fluid chamber 550. Asillustrated in FIG. 5B, the power source can be a fluid source stored atan elevation that is higher than that where the product fluid isrecovered 507. The difference in elevation 578 provides a natural sourceof pressure. During the power stroke, a valve 576 in the conduit isopened, allowing power fluid to flow from the power fluid source 570,through the conduit 546, and into the power fluid chamber 550. Thedifference in elevation 578 alone can cause the transfer piston 520 torise and pump fluid out of the pump outlet 506 at the recovery elevation507.

During the recovery stroke, the conduit valve 576, which is located atan elevation that is lower than the recovery elevation 507, is closedand a power fluid release valve 577 is opened. The power fluid releasevalve 577 is at an elevation that is lower than the elevation of theconduit valve 576. The power fluid release valve 577 is at an elevationlower than the product fluid recovery elevation 507, and the pressure inthe pump outlet line forces the transfer piston 520 down and power fluiddrains from the power fluid release valve 577.

Accordingly, in the embodiment illustrated in FIG. 5B, the oscillatingpressure is provided by alternating the conduit valve 576 and powerfluid release valve 577. The differences in elevation can be selecteddepending on the relative densities of the power fluid and the productfluid.

In some embodiments, the pumping apparatus comprises a power fluidcolumn internal to the product fluid. Such a design is advantageousbecause the power fluid can be supplied at a greater pressure withoutcompromising the structural integrity of the column containing the powerfluid. For example, if a pump is 3 inches in diameter, and if the powerfluid column is external to the product fluid column, then the diameterof the power fluid column is 3 inches. Since the force (F) exerted bythe power fluid on the wall of the power fluid column is determined bymultiplying the pressure (P) of the power fluid by the surface area ofthe column, and the surface area of a cylinder is determined bymultiplying the cylinder's circumference by its height, then the forceon an externally placed power fluid column is:

F _(external)=π(diameter)(Pressure)(height)=3Pπ(height)

Assuming the same 3 inch diameter pump uses a 1 inch diameter internalpower fluid column, the force on the power fluid column is:

F _(internal)=π(diameter)(pressure)(height)=1Pπ(height)

Assuming the height of the column is the same for each pump, theinternally placed power fluid column exerts only one third of the forceon the pump material when compared to the externally placed power fluidcolumn. For a pump constructed with a material capable of sustaining amaximum force, the power fluid can be supplied at 3 times the pressureif the power fluid column is internal rather than external.

Similarly, the hoop stress for a thin walled cylinder is equal to thepressure inside the cylinder multiplied by the radius of the cylinder,divided by the wall thickness. Accordingly, as the radius increases, thehoop stress increases linearly. In applications that require the powerfluid to be supplied at significant pressures, such as when pumpingfluid from very deep wells, it is preferable to have an internal powerfluid column. For example, for a water well at a depth of 10,000 feet,the power fluid can be supplied at a pressure of about 10,000 psi.

Below, Tables 1 through 20 include data compiled from the pumps of thepresent disclosure. In reference to the pipes of FIG. 5A and FIG. 5B,the data shows that the greater the diameter the conduit 546 the greaterthe (volume) required in the cylinder 572. The greater cylinder volumeis required to compensate for the greater amount of fluid compressionloss in the conduit 546. This fluid compression loss is linearlyproportional to the volume of the fluid in the conduit 546 for any givendrive pressure. Table 1 gives the bulk modulus value of typicalhydraulic water-based fluids and volume of fluid within differentconduit pipes for depths up to 4000 feet. Tables 2 through 10 illustratethe volumes of compression fluid losses for typical hydraulicwater-based fluids for given conduits (546) at different depths. Table 2illustrates the volume of fluid losses for a drive pressure of 500 psi.Table 3 illustrates the volume of fluid losses for a drive pressure of750 psi, etc. These volumes of water-based hydraulic fluid losses mustbe compensated by a corresponding increase in volume of the drivecylinder (572). Table 11 gives the bulk modulus value of typicalhydraulic oil-based fluids and volume of fluid within different conduitpipes for depths up to 4000 feet. Tables 12 through 20 illustrate thevolumes of compression fluid losses for typical hydraulic oil-basedfluids for given conduits (546) at different depths. Table 12illustrates the volume of fluid losses for a drive pressure of 500 psi.Table 13 illustrates the volume of fluid losses for a drive pressure of750 psi, etc. These volumes of oil-based hydraulic fluid losses must becompensated by a corresponding increase in volume of the drive cylinder(572).

TABLE 1 DATA for water Bulk Modulus = (psi) 300000 VOL. @ VOL. @ VOL. @VOL. @ VOL. @ OD ID WALL DEPTH DEPTH DEPTH DEPTH DEPTH PIPE OD AREA IDAREA THCK 500 750 1000 1250 1500 SIZE/SCHEDULE (in) (in{circumflex over( )}2) (in) (in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 0.405 0.129 0.2690.057 0.068 340.8 511.2 681.6 852.1 1022.5 1/4″ SCH 40 0.540 0.229 0.3640.104 0.088 624.1 936.1 1248.1 1560.1 1872.2 3/8″ SCH 40 0.675 0.3580.493 0.191 0.091 1144.8 1717.1 2289.5 2861.9 3434.3 1/2″ SCH 40 0.8400.554 0.622 0.304 0.109 1822.2 2733.3 3644.4 4555.6 5466.7 3/4″ SCH 401.050 0.865 0.824 0.533 0.113 3198.0 4797.0 6396.0 7994.9 9593.9 1″ SCH40 1.315 1.357 1.049 0.864 0.133 5182.9 7774.3 10365.8 12957.2 15548.7 11/4″ SCH 40 1.660 2.163 1.380 1.495 0.140 8969.7 13454.6 17939.4 22424.326909.2 1 1/2″ SCH 40 1.900 2.834 1.610 2.035 0.145 12208.8 18313.224417.6 30522.0 36626.4 1/8″ SCH 80 0.405 0.129 0.215 0.036 0.095 217.7326.6 435.4 544.3 653.2 1/4″ SCH 80 0.540 0.229 0.302 0.072 0.119 429.6644.4 859.1 1073.9 1288.7 3/8″ SCH 80 0.675 0.358 0.423 0.140 0.126842.8 1264.1 1685.5 2106.9 2528.3 1/2″ SCH 80 0.840 0.554 0.546 0.2340.147 1404.1 2106.2 2808.3 3510.3 4212.4 3/4″ SCH 80 1.050 0.865 0.7420.432 0.154 2593.2 3889.7 5186.3 6482.9 7779.5 1″ SCH 80 1.315 1.3570.957 0.719 0.179 4313.6 6470.5 8627.3 10784.1 12940.9 1 1/4″ SCH 801.660 2.163 1.278 1.282 0.191 7692.8 11539.2 15385.5 19231.9 23078.3 11/2″ SCH 80 1.900 2.834 1.500 1.766 0.200 10597.5 15896.3 21195.026493.8 31792.5 1/2″ SCH 160 0.840 0.554 0.464 0.169 0.188 1014.0 1521.12028.1 2535.1 3042.1 3/4″ SCH 160 1.050 0.865 0.612 0.294 0.219 1764.12646.2 3528.2 4410.3 5292.3 1″ SCH 160 1.315 1.357 0.815 0.521 0.2503128.5 4692.7 6257.0 7821.2 9385.5 1 1/4″ SCH 160 1.660 2.163 1.1601.056 0.250 6337.8 9506.7 12675.6 15844.4 19013.3 1 1/2″ SCH 160 1.9002.834 1.338 1.405 0.281 8432.0 12648.1 16864.1 21080.1 25296.1 VOL. @VOL. @ VOL. @ VOL. @ VOL. @ OD ID WALL DEPTH DEPTH DEPTH DEPTH DEPTHPIPE OD AREA ID AREA THCK 1750 2000 2250 2500 2750 SIZE/SCHEDULE (in)(in{circumflex over ( )}2) (in) (in{circumflex over ( )}2) (in)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″SCH 40 0.405 0.129 0.269 0.057 0.068 1192.9 1363.3 1533.7 1704.1 1874.51/4″ SCH 40 0.540 0.229 0.364 0.104 0.088 2184.2 2496.2 2808.3 3120.33432.3 3/8″ SCH 40 0.675 0.358 0.493 0.191 0.091 4006.7 4579.0 5151.45723.8 6296.2 1/2″ SCH 40 0.840 0.554 0.622 0.304 0.109 6377.8 7288.98200.0 9111.1 10022.2 3/4″ SCH 40 1.050 0.865 0.824 0.533 0.113 11192.912791.9 14390.9 15989.9 17588.9 1″ SCH 40 1.315 1.357 1.049 0.864 0.13318140.1 20731.6 23323.0 25914.4 28505.9 1 1/4″ SCH 40 1.660 2.163 1.3801.495 0.140 31394.0 35878.9 40363.8 44848.6 49333.5 1 1/2″ SCH 40 1.9002.834 1.610 2.035 0.145 42730.8 48835.2 54939.6 61044.0 67148.4 1/8″ SCH80 0.405 0.129 0.215 0.036 0.095 762.0 870.9 979.7 1088.6 1197.5 1/4″SCH 80 0.540 0.229 0.302 0.072 0.119 1503.5 1718.3 1933.1 2147.9 2362.63/8″ SCH 80 0.675 0.358 0.423 0.140 0.126 2949.6 3371.0 3792.4 4213.84635.2 1/2″ SCH 80 0.840 0.554 0.546 0.234 0.147 4914.4 5616.5 6318.67020.6 7722.7 3/4″ SCH 80 1.050 0.865 0.742 0.432 0.154 9076.0 10372.611669.2 12965.8 14262.4 1″ SCH 80 1.315 1.357 0.957 0.719 0.179 15097.817254.6 19411.4 21568.2 23725.1 1 1/4″ SCH 80 1.660 2.163 1.278 1.2820.191 26924.7 30771.1 34617.5 38463.8 42310.2 1 1/2″ SCH 80 1.900 2.8341.500 1.766 0.200 37091.3 42390.0 47688.8 52987.5 58286.3 1/2″ SCH 1600.840 0.554 0.464 0.169 0.188 3549.2 4056.2 4563.2 5070.2 5577.2 3/4″SCH 160 1.050 0.865 0.612 0.294 0.219 6174.4 7056.4 7938.5 8820.5 9702.61″ SCH 160 1.315 1.357 0.815 0.521 0.250 10949.7 12514.0 14078.2 15642.517206.7 1 1/4″ SCH 160 1.660 2.163 1.160 1.056 0.250 22182.2 25351.128520.0 31688.9 34857.8 1 1/2″ SCH 160 1.900 2.834 1.338 1.405 0.28129512.2 33728.2 37944.2 42160.2 46376.3 VOL. @ VOL. @ VOL. @ VOL. @ VOL.@ OD ID WALL DEPTH DEPTH DEPTH DEPTH DEPTH PIPE OD AREA ID AREA THCK3000 3250 3500 3750 4000 SIZE/SCHEDULE (in) (in{circumflex over ( )}2)(in) (in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 0.405 0.129 0.2690.057 0.068 2044.9 2215.3 2385.7 2556.2 2726.6 1/4″ SCH 40 0.540 0.2290.364 0.104 0.088 3744.3 4056.4 4368.4 4680.4 4992.4 3/8″ SCH 40 0.6750.358 0.493 0.191 0.091 6868.6 7440.9 8013.3 8585.7 9158.1 1/2″ SCH 400.840 0.554 0.622 0.304 0.109 10933.3 11844.5 12755.6 13666.7 14577.83/4″ SCH 40 1.050 0.865 0.824 0.533 0.113 19187.9 20786.9 22385.823984.8 25583.8 1″ SCH 40 1.315 1.357 1.049 0.864 0.133 31097.3 33688.836280.2 38871.7 41463.1 1 1/4″ SCH 40 1.660 2.163 1.380 1.495 0.14053818.3 58303.2 62788.1 67272.9 71757.8 1 1/2″ SCH 40 1.900 2.834 1.6102.035 0.145 73252.7 79357.1 85461.5 91565.9 97670.3 1/8″ SCH 80 0.4050.129 0.215 0.036 0.095 1306.3 1415.2 1524.0 1632.9 1741.8 1/4″ SCH 800.540 0.229 0.302 0.072 0.119 2577.4 2792.2 3007.0 3221.8 3436.6 3/8″SCH 80 0.675 0.358 0.423 0.140 0.126 5056.5 5477.9 5899.3 6320.7 6742.01/2″ SCH 80 0.840 0.554 0.546 0.234 0.147 8424.8 9126.8 9828.9 10530.911233.0 3/4″ SCH 80 1.050 0.865 0.742 0.432 0.154 15558.9 16855.518152.1 19448.7 20745.3 1″ SCH 80 1.315 1.357 0.957 0.719 0.179 25881.928038.7 30195.5 32352.4 34509.2 1 1/4″ SCH 80 1.660 2.163 1.278 1.2820.191 46156.6 50003.0 53849.4 57695.8 61542.1 1 1/2″ SCH 80 1.900 2.8341.500 1.766 0.200 63585.0 68883.8 74182.5 79481.3 84780.0 1/2″ SCH 1600.840 0.554 0.464 0.169 0.188 6084.3 6591.3 7098.3 7605.3 8112.4 3/4″SCH 160 1.050 0.865 0.612 0.294 0.219 10584.6 11466.7 12348.7 13230.814112.8 1″ SCH 160 1.315 1.357 0.815 0.521 0.250 18771.0 20335.2 21899.523463.7 25028.0 1 1/4″ SCH 160 1.660 2.163 1.160 1.056 0.250 38026.741195.5 44364.4 47533.3 50702.2 1 1/2″ SCH 160 1.900 2.834 1.338 1.4050.281 50592.3 54808.3 59024.3 63240.4 67456.4

TABLE 2 Drive Delta-P = (psi) 500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′1250′ 1500′ 1750′ 2000′ 2250′ SIZE/SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 0.60.9 1.1 1.4 1.7 2.0 2.3 2.6 1/4″ SCH 40 1.0 1.6 2.1 2.6 3.1 3.6 4.2 4.73/8″ SCH 40 1.9 2.9 3.8 4.8 5.7 6.7 7.6 8.6 1/2″ SCH 40 3.0 4.6 6.1 7.69.1 10.6 12.1 13.7 3/4″ SCH 40 5.3 8.0 10.7 13.3 16.0 18.7 21.3 24.0 1″SCH 40 8.6 13.0 17.3 21.6 25.9 30.2 34.6 38.9 1 1/4″ SCH 40 14.9 22.429.9 37.4 44.8 52.3 59.8 67.3 1 1/2″ SCH 40 20.3 30.5 40.7 50.9 61.071.2 81.4 91.6 1/8″ SCH 80 0.4 0.5 0.7 0.9 1.1 1.3 1.5 1.6 1/4″ SCH 800.7 1.1 1.4 1.8 2.1 2.5 2.9 3.2 3/8″ SCH 80 1.4 2.1 2.8 3.5 4.2 4.9 5.66.3 1/2″ SCH 80 2.3 3.5 4.7 5.9 7.0 8.2 9.4 10.5 3/4″ SCH 80 4.3 6.5 8.610.8 13.0 15.1 17.3 19.4 1″ SCH 80 7.2 10.8 14.4 18.0 21.6 25.2 28.832.4 1 1/4″ SCH 80 12.8 19.2 25.6 32.1 38.5 44.9 51.3 57.7 1 1/2″ SCH 8017.7 26.5 35.3 44.2 53.0 61.8 70.7 79.5 1/2″ SCH 160 1.7 2.5 3.4 4.2 5.15.9 6.8 7.6 3/4″ SCH 160 2.9 4.4 5.9 7.4 8.8 10.3 11.8 13.2 1″ SCH 1605.2 7.8 10.4 13.0 15.6 18.2 20.9 23.5 1 1/4″ SCH 160 10.6 15.8 21.1 26.431.7 37.0 42.3 47.5 1 1/2″ SCH 160 14.1 21.1 28.1 35.1 42.2 49.2 56.263.2 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ PIPE 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SIZE/SCHEDULE(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 2.83.1 3.4 3.7 4.0 4.3 4.5 1/4″ SCH 40 5.2 5.7 6.2 6.8 7.3 7.8 8.3 3/8″ SCH40 9.5 10.5 11.4 12.4 13.4 14.3 15.3 1/2″ SCH 40 15.2 16.7 18.2 19.721.3 22.8 24.3 3/4″ SCH 40 26.6 29.3 32.0 34.6 37.3 40.0 42.6 1″ SCH 4043.2 47.5 51.8 56.1 60.5 64.8 69.1 1 1/4″ SCH 40 74.7 82.2 89.7 97.2104.6 112.1 119.6 1 1/2″ SCH 40 101.7 111.9 122.1 132.3 142.4 152.6162.8 1/8″ SCH 80 1.8 2.0 2.2 2.4 2.5 2.7 2.9 1/4″ SCH 80 3.6 3.9 4.34.7 5.0 5.4 5.7 3/8″ SCH 80 7.0 7.7 8.4 9.1 9.8 10.5 11.2 1/2″ SCH 8011.7 12.9 14.0 15.2 16.4 17.6 18.7 3/4″ SCH 80 21.6 23.8 25.9 28.1 30.332.4 34.6 1″ SCH 80 35.9 39.5 43.1 46.7 50.3 53.9 57.5 1 1/4″ SCH 8064.1 70.5 76.9 83.3 89.7 96.2 102.6 1 1/2″ SCH 80 88.3 97.1 106.0 114.8123.6 132.5 141.3 1/2″ SCH 160 8.5 9.3 10.1 11.0 11.8 12.7 13.5 3/4″ SCH160 14.7 16.2 17.6 19.1 20.6 22.1 23.5 1″ SCH 160 26.1 28.7 31.3 33.936.5 39.1 41.7 1 1/4″ SCH 160 52.8 58.1 63.4 68.7 73.9 79.2 84.5 1 1/2″SCH 160 70.3 77.3 84.3 91.3 98.4 105.4 112.4

TABLE 3 Drive Delta-P = (psi) 750 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′1250' 1500′ 1750′ 2000′ 2250′ SIZE/SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 0.91.3 1.7 2.1 2.6 3.0 3.4 3.8 1/4″ SCH 40 1.6 2.3 3.1 3.9 4.7 5.5 6.2 7.03/8″ SCH 40 2.9 4.3 5.7 7.2 8.6 10.0 11.4 12.9 1/2″ SCH 40 4.6 6.8 9.111.4 13.7 15.9 18.2 20.5 3/4″ SCH 40 8.0 12.0 16.0 20.0 24.0 28.0 32.036.0 1″ SCH 40 13.0 19.4 25.9 32.4 38.9 45.4 51.8 58.3 1 1/4″ SCH 4022.4 33.6 44.8 56.1 67.3 78.5 89.7 100.9 1 1/2″ SCH 40 30.5 45.8 61.076.3 91.6 106.8 122.1 137.3 1/8″ SCH 80 0.5 0.8 1.1 1.4 1.6 1.9 2.2 2.41/4″ SCH 80 1.1 1.6 2.1 2.7 3.2 3.8 4.3 4.8 3/8″ SCH 80 2.1 3.2 4.2 5.36.3 7.4 8.4 9.5 1/2″ SCH 80 3.5 5.3 7.0 8.8 10.5 12.3 14.0 15.8 3/4″ SCH80 6.5 9.7 13.0 16.2 19.4 22.7 25.9 29.2 1″ SCH 80 10.8 16.2 21.6 27.032.4 37.7 43.1 48.5 1 1/4″ SCH 80 19.2 28.8 38.5 48.1 57.7 67.3 76.986.5 1 1/2″ SCH 80 26.5 39.7 53.0 66.2 79.5 92.7 106.0 119.2 1/2″ SCH160 2.5 3.8 5.1 6.3 7.6 8.9 10.1 11.4 3/4″ SCH 160 4.4 6.6 8.8 11.0 13.215.4 17.6 19.8 1″ SCH 160 7.8 11.7 15.6 19.6 23.5 27.4 31.3 35.2 1 1/4″SCH 160 15.8 23.8 31.7 39.6 47.5 55.5 63.4 71.3 1 1/2″ SCH 160 21.1 31.642.2 52.7 63.2 73.8 84.3 94.9 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEVOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ PIPE 2500′ 2750′ 3000′ 3250′ 3500′ 3750′4000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 4.3 4.7 5.1 5.5 6.0 6.4 6.8 1/4″ SCH 40 7.8 8.69.4 10.1 10.9 11.7 12.5 3/8″ SCH 40 14.3 15.7 17.2 18.6 20.0 21.5 22.91/2″ SCH 40 22.8 25.1 27.3 29.6 31.9 34.2 36.4 3/4″ SCH 40 40.0 44.048.0 52.0 56.0 60.0 64.0 1″ SCH 40 64.8 71.3 77.7 84.2 90.7 97.2 103.7 11/4″ SCH 40 112.1 123.3 134.5 145.8 157.0 168.2 179.4 1 1/2″ SCH 40152.6 167.9 183.1 198.4 213.7 228.9 244.2 1/8″ SCH 80 2.7 3.0 3.3 3.53.8 4.1 4.4 1/4″ SCH 80 5.4 5.9 6.4 7.0 7.5 8.1 8.6 3/8″ SCH 80 10.511.6 12.6 13.7 14.7 15.8 16.9 1/2″ SCH 80 17.6 19.3 21.1 22.8 24.6 26.328.1 3/4″ SCH 80 32.4 35.7 38.9 42.1 45.4 48.6 51.9 1″ SCH 80 53.9 59.364.7 70.1 75.5 80.9 86.3 1 1/4″ SCH 80 96.2 105.8 115.4 125.0 134.6144.2 153.9 1 1/2″ SCH 80 132.5 145.7 159.0 172.2 185.5 198.7 212.0 1/2″SCH 160 12.7 13.9 15.2 16.5 17.7 19.0 20.3 3/4″ SCH 160 22.1 24.3 26.528.7 30.9 33.1 35.3 1″ SCH 160 39.1 43.0 46.9 50.8 54.7 58.7 62.6 1 1/4″SCH 160 79.2 87.1 95.1 103.0 110.9 118.8 126.8 1 1/2″ SCH 160 105.4115.9 126.5 137.0 147.6 158.1 168.6

TABLE 4 Drive Delta-P = (psi) 1000 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 1.1 1.7 2.3 2.8 3.4 4.0 4.5 1/4″ SCH 40 2.1 3.14.2 5.2 6.2 7.3 8.3 3/8″ SCH 40 3.8 5.7 7.6 9.5 11.4 13.4 15.3 1/2″ SCH40 6.1 9.1 12.1 15.2 18.2 21.3 24.3 3/4″ SCH 40 10.7 16.0 21.3 26.6 32.037.3 42.6 1″ SCH 40 17.3 25.9 34.6 43.2 51.8 60.5 69.1 1 1/4″ SCH 4029.9 44.8 59.8 74.7 89.7 104.6 119.6 1 1/2″ SCH 40 40.7 61.0 81.4 101.7122.1 142.4 162.8 1/8″ SCH 80 0.7 1.1 1.5 1.8 2.2 2.5 2.9 1/4″ SCH 801.4 2.1 2.9 3.6 4.3 5.0 5.7 3/8″ SCH 80 2.8 4.2 5.6 7.0 8.4 9.8 11.21/2″ SCH 80 4.7 7.0 9.4 11.7 14.0 16.4 18.7 3/4″ SCH 80 8.6 13.0 17.321.6 25.9 30.3 34.6 1″ SCH 80 14.4 21.6 28.8 35.9 43.1 50.3 57.5 1 1/4″SCH 80 25.6 38.5 51.3 64.1 76.9 89.7 102.6 1 1/2″ SCH 80 35.3 53.0 70.788.3 106.0 123.6 141.3 1/2″ SCH 160 3.4 5.1 6.8 8.5 10.1 11.8 13.5 3/4″SCH 160 5.9 8.8 11.8 14.7 17.6 20.6 23.5 1″ SCH 160 10.4 15.6 20.9 26.131.3 36.5 41.7 1 1/4″ SCH 160 21.1 31.7 42.3 52.8 63.4 73.9 84.5 1 1/2″SCH 160 28.1 42.2 56.2 70.3 84.3 98.4 112.4 DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUMEVOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE2250′ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SIZE/SCHEDULE(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 5.1 5.7 6.2 6.8 7.4 8.0 8.5 9.1 1/4″ SCH 40 9.410.4 11.4 12.5 13.5 14.6 15.6 16.6 3/8″ SCH 40 17.2 19.1 21.0 22.9 24.826.7 28.6 30.5 1/2″ SCH 40 27.3 30.4 33.4 36.4 39.5 42.5 45.6 48.6 3/4″SCH 40 48.0 53.3 58.6 64.0 69.3 74.6 79.9 85.3 1″ SCH 40 77.7 86.4 95.0103.7 112.3 120.9 129.6 138.2 1 1/4″ SCH 40 134.5 149.5 164.4 179.4194.3 209.3 224.2 239.2 1 1/2″ SCH 40 183.1 203.5 223.8 244.2 264.5284.9 305.2 325.6 1/8″ SCH 80 3.3 3.6 4.0 4.4 4.7 5.1 5.4 5.8 1/4″ SCH80 6.4 7.2 7.9 8.6 9.3 10.0 10.7 11.5 3/8″ SCH 80 12.6 14.0 15.5 16.918.3 19.7 21.1 22.5 1/2″ SCH 80 21.1 23.4 25.7 28.1 30.4 32.8 35.1 37.43/4″ SCH 80 38.9 43.2 47.5 51.9 56.2 60.5 64.8 69.2 1″ SCH 80 64.7 71.979.1 86.3 93.5 100.7 107.8 115.0 1 1/4″ SCH 80 115.4 128.2 141.0 153.9166.7 179.5 192.3 205.1 1 1/2″ SCH 80 159.0 176.6 194.3 212.0 229.6247.3 264.9 282.6 1/2″ SCH 160 15.2 16.9 18.6 20.3 22.0 23.7 25.4 27.03/4″ SCH 160 26.5 29.4 32.3 35.3 38.2 41.2 44.1 47.0 1″ SCH 160 46.952.1 57.4 62.6 67.8 73.0 78.2 83.4 1 1/4″ SCH 160 95.1 105.6 116.2 126.8137.3 147.9 158.4 169.0 1 1/2″ SCH 160 126.5 140.5 154.6 168.6 182.7196.7 210.8 224.9

TABLE 5 Drive Delta-P = (psi) 1250 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 1.4 2.1 2.8 3.6 4.3 5.0 5.7 1/4″ SCH 40 2.6 3.95.2 6.5 7.8 9.1 10.4 3/8″ SCH 40 4.8 7.2 9.5 11.9 14.3 16.7 19.1 1/2″SCH 40 7.6 11.4 15.2 19.0 22.8 26.6 30.4 3/4″ SCH 40 13.3 20.0 26.6 33.340.0 46.6 53.3 1″ SCH 40 21.6 32.4 43.2 54.0 64.8 75.6 86.4 1 1/4″ SCH40 37.4 56.1 74.7 93.4 112.1 130.8 149.5 1 1/2″ SCH 40 50.9 76.3 101.7127.2 152.6 178.0 203.5 1/8″ SCH 80 0.9 1.4 1.8 2.3 2.7 3.2 3.6 1/4″ SCH80 1.8 2.7 3.6 4.5 5.4 6.3 7.2 3/8″ SCH 80 3.5 5.3 7.0 8.8 10.5 12.314.0 1/2″ SCH 80 5.9 8.8 11.7 14.6 17.6 20.5 23.4 3/4″ SCH 80 10.8 16.221.6 27.0 32.4 37.8 43.2 1″ SCH 80 18.0 27.0 35.9 44.9 53.9 62.9 71.9 11/4″ SCH 80 32.1 48.1 64.1 80.1 96.2 112.2 128.2 1 1/2″ SCH 80 44.2 66.288.3 110.4 132.5 154.5 176.6 1/2″ SCH 160 4.2 6.3 8.5 10.6 12.7 14.816.9 3/4″ SCH 160 7.4 11.0 14.7 18.4 22.1 25.7 29.4 1″ SCH 160 13.0 19.626.1 32.6 39.1 45.6 52.1 1 1/4″ SCH 160 26.4 39.6 52.8 66.0 79.2 92.4105.6 1 1/2″ SCH 160 35.1 52.7 70.3 87.8 105.4 123.0 140.5 DRIVE DRIVEDRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ PIPE 2250′ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) 1/8″ SCH 40 6.4 7.1 7.8 8.5 9.2 9.9 10.7 11.41/4″ SCH 40 11.7 13.0 14.3 15.6 16.9 18.2 19.5 20.8 3/8″ SCH 40 21.523.8 26.2 28.6 31.0 33.4 35.8 38.2 1/2″ SCH 40 34.2 38.0 41.8 45.6 49.453.1 56.9 60.7 3/4″ SCH 40 60.0 66.6 73.3 79.9 86.6 93.3 99.9 106.6 1″SCH 40 97.2 108.0 118.8 129.6 140.4 151.2 162.0 172.8 1 1/4″ SCH 40168.2 186.9 205.6 224.2 242.9 261.6 280.3 299.0 1 1/2″ SCH 40 228.9254.3 279.8 305.2 330.7 356.1 381.5 407.0 1/8″ SCH 80 4.1 4.5 5.0 5.45.9 6.4 6.8 7.3 1/4″ SCH 80 8.1 8.9 9.8 10.7 11.6 12.5 13.4 14.3 3/8″SCH 80 15.8 17.6 19.3 21.1 22.8 24.6 26.3 28.1 1/2″ SCH 80 26.3 29.332.2 35.1 38.0 41.0 43.9 46.8 3/4″ SCH 80 48.6 54.0 59.4 64.8 70.2 75.681.0 86.4 1″ SCH 80 80.9 89.9 98.9 107.8 116.8 125.8 134.8 143.8 1 1/4″SCH 80 144.2 160.3 176.3 192.3 208.3 224.4 240.4 256.4 1 1/2″ SCH 80198.7 220.8 242.9 264.9 287.0 309.1 331.2 353.3 1/2″ SCH 160 19.0 21.123.2 25.4 27.5 29.6 31.7 33.8 3/4″ SCH 160 33.1 36.8 40.4 44.1 47.8 51.555.1 58.8 1″ SCH 160 58.7 65.2 71.7 78.2 84.7 91.2 97.8 104.3 1 1/4″ SCH160 118.8 132.0 145.2 158.4 171.6 184.9 198.1 211.3 1 1/2″ SCH 160 158.1175.7 193.2 210.8 228.4 245.9 263.5 281.1

TABLE 6 Drive Delta-P = (psi) 1500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME V OLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 1.7 2.6 3.4 4.3 5.1 6.0 6.8 1/4″ SCH 40 3.1 4.76.2 7.8 9.4 10.9 12.5 3/8″ SCH 40 5.7 8.6 11.4 14.3 17.2 20.0 22.9 1/2″SCH 40 9.1 13.7 18.2 22.8 27.3 31.9 36.4 3/4″ SCH 40 16.0 24.0 32.0 40.048.0 56.0 64.0 1″ SCH 40 25.9 38.9 51.8 64.8 77.7 90.7 103.7 1 1/4″ SCH40 44.8 67.3 89.7 112.1 134.5 157.0 179.4 1 1/2″ SCH 40 61.0 91.6 122.1152.6 183.1 213.7 244.2 1/8″ SCH 80 1.1 1.6 2.2 2.7 3.3 3.8 4.4 1/4″ SCH80 2.1 3.2 4.3 5.4 6.4 7.5 8.6 3/8″ SCH 80 4.2 6.3 8.4 10.5 12.6 14.716.9 1/2″ SCH 80 7.0 10.5 14.0 17.6 21.1 24.6 28.1 3/4″ SCH 80 13.0 19.425.9 32.4 38.9 45.4 51.9 1″ SCH 80 21.6 32.4 43.1 53.9 64.7 75.5 86.3 11/4″ SCH 80 38.5 57.7 76.9 96.2 115.4 134.6 153.9 1 1/2″ SCH 80 53.079.5 106.0 132.5 159.0 185.5 212.0 1/2″ SCH 160 5.1 7.6 10.1 12.7 15.217.7 20.3 3/4″ SCH 160 8.8 13.2 17.6 22.1 26.5 30.9 35.3 1″ SCH 160 15.623.5 31.3 39.1 46.9 54.7 62.6 1 1/4″ SCH 160 31.7 47.5 63.4 79.2 95.1110.9 126.8 1 1/2″ SCH 160 42.2 63.2 84.3 105.4 126.5 147.6 168.6 DRIVEDRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ LOSS @ PIPE 2250′ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) 1/8″ SCH 40 7.7 8.5 9.4 10.2 11.1 11.9 12.813.6 1/4″ SCH 40 14.0 15.6 17.2 18.7 20.3 21.8 23.4 25.0 3/8″ SCH 4025.8 28.6 31.5 34.3 37.2 40.1 42.9 45.8 1/2″ SCH 40 41.0 45.6 50.1 54.759.2 63.8 68.3 72.9 3/4″ SCH 40 72.0 79.9 87.9 95.9 103.9 111.9 119.9127.9 1″ SCH 40 116.6 129.6 142.5 155.5 168.4 181.4 194.4 207.3 1 1/4″SCH 40 201.8 224.2 246.7 269.1 291.5 313.9 336.4 358.8 1 1/2″ SCH 40274.7 305.2 335.7 366.3 396.8 427.3 457.8 488.4 1/8″ SCH 80 4.9 5.4 6.06.5 7.1 7.6 8.2 8.7 1/4″ SCH 80 9.7 10.7 11.8 12.9 14.0 15.0 16.1 17.23/8″ SCH 80 19.0 21.1 23.2 25.3 27.4 29.5 31.6 33.7 1/2″ SCH 80 31.635.1 38.6 42.1 45.6 49.1 52.7 56.2 3/4″ SCH 80 58.3 64.8 71.3 77.8 84.390.8 97.2 103.7 1″ SCH 80 97.1 107.8 118.6 129.4 140.2 151.0 161.8 172.51 1/4″ SCH 80 173.1 192.3 211.6 230.8 250.0 269.2 288.5 307.7 1 1/2″ SCH80 238.4 264.9 291.4 317.9 344.4 370.9 397.4 423.9 1/2″ SCH 160 22.825.4 27.9 30.4 33.0 35.5 38.0 40.6 3/4″ SCH 160 39.7 44.1 48.5 52.9 57.361.7 66.2 70.6 1″ SCH 160 70.4 78.2 86.0 93.9 101.7 109.5 117.3 125.1 11/4″ SCH 160 142.6 158.4 174.3 190.1 206.0 221.8 237.7 253.5 1 1/2″ SCH160 189.7 210.8 231.9 253.0 274.0 295.1 316.2 337.3

TABLE 7 Drive Delta-P = (psi) 1750 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 2.0 3.0 4.0 5.0 6.0 7.0 8.0 1/4″ SCH 40 3.6 5.57.3 9.1 10.9 12.7 14.6 3/8″ SCH 40 6.7 10.0 13.4 16.7 20.0 23.4 26.71/2″ SCH 40 10.6 15.9 21.3 26.6 31.9 37.2 42.5 3/4″ SCH 40 18.7 28.037.3 46.6 56.0 65.3 74.6 1″ SCH 40 30.2 45.4 60.5 75.6 90.7 105.8 120.91 1/4″ SCH 40 52.3 78.5 104.6 130.8 157.0 183.1 209.3 1 1/2″ SCH 40 71.2106.8 142.4 178.0 213.7 249.3 284.9 1/8″ SCH 80 1.3 1.9 2.5 3.2 3.8 4.45.1 1/4″ SCH 80 2.5 3.8 5.0 6.3 7.5 8.8 10.0 3/8″ SCH 80 4.9 7.4 9.812.3 14.7 17.2 19.7 1/2″ SCH 80 8.2 12.3 16.4 20.5 24.6 28.7 32.8 3/4″SCH 80 15.1 22.7 30.3 37.8 45.4 52.9 60.5 1″ SCH 80 25.2 37.7 50.3 62.975.5 88.1 100.7 1 1/4″ SCH 80 44.9 67.3 89.7 112.2 134.6 157.1 179.5 11/2″ SCH 80 61.8 92.7 123.6 154.5 185.5 216.4 247.3 1/2″ SCH 160 5.9 8.911.8 14.8 17.7 20.7 23.7 3/4″ SCH 160 10.3 15.4 20.6 25.7 30.9 36.0 41.21″ SCH 160 18.2 27.4 36.5 45.6 54.7 63.9 73.0 1 1/4″ SCH 160 37.0 55.573.9 92.4 110.9 129.4 147.9 1 1/2″ SCH 160 49.2 73.8 98.4 123.0 147.6172.2 196.7 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUMEVOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 2250′ 2500′ 2750′ 3000′ 3250′3500′ 3750′ 4000′ SIZE/SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 8.99.9 10.9 11.9 12.9 13.9 14.9 15.9 1/4″ SCH 40 16.4 18.2 20.0 21.8 23.725.5 27.3 29.1 3/8″ SCH 40 30.0 33.4 36.7 40.1 43.4 46.7 50.1 53.4 1/2″SCH 40 47.8 53.1 58.5 63.8 69.1 74.4 79.7 85.0 3/4″ SCH 40 83.9 93.3102.6 111.9 121.3 130.6 139.9 149.2 1″ SCH 40 136.1 151.2 166.3 181.4196.5 211.6 226.8 241.9 1 1/4″ SCH 40 235.5 261.6 287.8 313.9 340.1366.3 392.4 418.6 1 1/2″ SCH 40 320.5 356.1 391.7 427.3 462.9 498.5534.1 569.7 1/8″ SCH 80 5.7 6.4 7.0 7.6 8.3 8.9 9.5 10.2 1/4″ SCH 8011.3 12.5 13.8 15.0 16.3 17.5 18.8 20.0 3/8″ SCH 80 22.1 24.6 27.0 29.532.0 34.4 36.9 39.3 1/2″ SCH 80 36.9 41.0 45.0 49.1 53.2 57.3 61.4 65.53/4″ SCH 80 68.1 75.6 83.2 90.8 98.3 105.9 113.5 121.0 1″ SCH 80 113.2125.8 138.4 151.0 163.6 176.1 188.7 201.3 1 1/4″ SCH 80 201.9 224.4246.8 269.2 291.7 314.1 336.6 359.0 1 1/2″ SCH 80 278.2 309.1 340.0370.9 401.8 432.7 463.6 494.6 1/2″ SCH 160 26.6 29.6 32.5 35.5 38.4 41.444.4 47.3 3/4″ SCH 160 46.3 51.5 56.6 61.7 66.9 72.0 77.2 82.3 1″ SCH160 82.1 91.2 100.4 109.5 118.6 127.7 136.9 146.0 1 1/4″ SCH 160 166.4184.9 203.3 221.8 240.3 258.8 277.3 295.8 1 1/2″ SCH 160 221.3 245.9270.5 295.1 319.7 344.3 368.9 393.5

TABLE 8 Drive Delta-P = (psi) 2000 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 2.3 3.4 4.5 5.7 6.8 8.0 9.1 1/4″ SCH 40 4.2 6.28.3 10.4 12.5 14.6 16.6 3/8″ SCH 40 7.6 11.4 15.3 19.1 22.9 26.7 30.51/2″ SCH 40 12.1 18.2 24.3 30.4 36.4 42.5 48.6 3/4″ SCH 40 21.3 32.042.6 53.3 64.0 74.6 85.3 1″ SCH 40 34.6 51.8 69.1 86.4 103.7 120.9 138.21 1/4″ SCH 40 59.8 89.7 119.6 149.5 179.4 209.3 239.2 1 1/2″ SCH 40 81.4122.1 162.8 203.5 244.2 284.9 325.6 1/8″ SCH 80 1.5 2.2 2.9 3.6 4.4 5.15.8 1/4″ SCH 80 2.9 4.3 5.7 7.2 8.6 10.0 11.5 3/8″ SCH 80 5.6 8.4 11.214.0 16.9 19.7 22.5 1/2″ SCH 80 9.4 14.0 18.7 23.4 28.1 32.8 37.4 3/4″SCH 80 17.3 25.9 34.6 43.2 51.9 60.5 69.2 1″ SCH 80 28.8 43.1 57.5 71.986.3 100.7 115.0 1 1/4″ SCH 80 51.3 76.9 102.6 128.2 153.9 179.5 205.1 11/2″ SCH 80 70.7 106.0 141.3 176.6 212.0 247.3 282.6 1/2″ SCH 160 6.810.1 13.5 16.9 20.3 23.7 27.0 3/4″ SCH 160 11.8 17.6 23.5 29.4 35.3 41.247.0 1″ SCH 160 20.9 31.3 41.7 52.1 62.6 73.0 83.4 1 1/4″ SCH 160 42.363.4 84.5 105.6 126.8 147.9 169.0 1 1/2″ SCH 160 56.2 84.3 112.4 140.5168.6 196.7 224.9 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUMEVOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 2250′ 2500′ 2750′ 3000′ 3250′3500′ 3750′ 4000′ SIZE/SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 10.211.4 12.5 13.6 14.8 15.9 17.0 18.2 1/4″ SCH 40 18.7 20.8 22.9 25.0 27.029.1 31.2 33.3 3/8″ SCH 40 34.3 38.2 42.0 45.8 49.6 53.4 57.2 61.1 1/2″SCH 40 54.7 60.7 66.8 72.9 79.0 85.0 91.1 97.2 3/4″ SCH 40 95.9 106.6117.3 127.9 138.6 149.2 159.9 170.6 1″ SCH 40 155.5 172.8 190.0 207.3224.6 241.9 259.1 276.4 1 1/4″ SCH 40 269.1 299.0 328.9 358.8 388.7418.6 448.5 478.4 1 1/2″ SCH 40 366.3 407.0 447.7 488.4 529.0 569.7610.4 651.1 1/8″ SCH 80 6.5 7.3 8.0 8.7 9.4 10.2 10.9 11.6 1/4″ SCH 8012.9 14.3 15.8 17.2 18.6 20.0 21.5 22.9 3/8″ SCH 80 25.3 28.1 30.9 33.736.5 39.3 42.1 44.9 1/2″ SCH 80 42.1 46.8 51.5 56.2 60.8 65.5 70.2 74.93/4″ SCH 80 77.8 86.4 95.1 103.7 112.4 121.0 129.7 138.3 1″ SCH 80 129.4143.8 158.2 172.5 186.9 201.3 215.7 230.1 1 1/4″ SCH 80 230.8 256.4282.1 307.7 333.4 359.0 384.6 410.3 1 1/2″ SCH 80 317.9 353.3 388.6423.9 459.2 494.6 529.9 565.2 1/2″ SCH 160 30.4 33.8 37.2 40.6 43.9 47.350.7 54.1 3/4″ SCH 160 52.9 58.8 64.7 70.6 76.4 82.3 88.2 94.1 1″ SCH160 93.9 104.3 114.7 125.1 135.6 146.0 156.4 166.9 1 1/4″ SCH 160 190.1211.3 232.4 253.5 274.6 295.8 316.9 338.0 1 1/2″ SCH 160 253.0 281.1309.2 337.3 365.4 393.5 421.6 449.7

TABLE 9 Drive Delta-P = (psi) 2250 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 2.6 3.8 5.1 6.4 7.7 8.9 10.2 1/4″ SCH 40 4.7 7.09.4 11.7 14.0 16.4 18.7 3/8″ SCH 40 8.6 12.9 17.2 21.5 25.8 30.0 34.31/2″ SCH 40 13.7 20.5 27.3 34.2 41.0 47.8 54.7 3/4″ SCH 40 24.0 36.048.0 60.0 72.0 83.9 95.9 1″ SCH 40 38.9 58.3 77.7 97.2 116.6 136.1 155.51 1/4″ SCH 40 67.3 100.9 134.5 168.2 201.8 235.5 269.1 1 1/2″ SCH 4091.6 137.3 183.1 228.9 274.7 320.5 366.3 1/8″ SCH 80 1.6 2.4 3.3 4.1 4.95.7 6.5 1/4″ SCH 80 3.2 4.8 6.4 8.1 9.7 11.3 12.9 3/8″ SCH 80 6.3 9.512.6 15.8 19.0 22.1 25.3 1/2″ SCH 80 10.5 15.8 21.1 26.3 31.6 36.9 42.13/4″ SCH 80 19.4 29.2 38.9 48.6 58.3 68.1 77.8 1″ SCH 80 32.4 48.5 64.780.9 97.1 113.2 129.4 1 1/4″ SCH 80 57.7 86.5 115.4 144.2 173.1 201.9230.8 1 1/2″ SCH 80 79.5 119.2 159.0 198.7 238.4 278.2 317.9 1/2″ SCH160 7.6 11.4 15.2 19.0 22.8 26.6 30.4 3/4″ SCH 160 13.2 19.8 26.5 33.139.7 46.3 52.9 1″ SCH 160 23.5 35.2 46.9 58.7 70.4 82.1 93.9 1 1/4″ SCH160 47.5 71.3 95.1 118.8 142.6 166.4 190.1 1 1/2″ SCH 160 63.2 94.9126.5 158.1 189.7 221.3 253.0 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 2250′ 2500′ 2750′3000′ 3250′ 3500′ 3750′ 4000′ SIZE/SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 11.512.8 14.1 15.3 16.6 17.9 19.2 20.4 1/4″ SCH 40 21.1 23.4 25.7 28.1 30.432.8 35.1 37.4 3/8″ SCH 40 38.6 42.9 47.2 51.5 55.8 60.1 64.4 68.7 1/2″SCH 40 61.5 68.3 75.2 82.0 88.8 95.7 102.5 109.3 3/4″ SCH 40 107.9 119.9131.9 143.9 155.9 167.9 179.9 191.9 1″ SCH 40 174.9 194.4 213.8 233.2252.7 272.1 291.5 311.0 1 1/4″ SCH 40 302.7 336.4 370.0 403.6 437.3470.9 504.5 538.2 1 1/2″ SCH 40 412.0 457.8 503.6 549.4 595.2 641.0686.7 732.5 1/8″ SCH 80 7.3 8.2 9.0 9.8 10.6 11.4 12.2 13.1 1/4″ SCH 8014.5 16.1 17.7 19.3 20.9 22.6 24.2 25.8 3/8″ SCH 80 28.4 31.6 34.8 37.941.1 44.2 47.4 50.6 1/2″ SCH 80 47.4 52.7 57.9 63.2 68.5 73.7 79.0 84.23/4″ SCH 80 87.5 97.2 107.0 116.7 126.4 136.1 145.9 155.6 1″ SCH 80145.6 161.8 177.9 194.1 210.3 226.5 242.6 258.8 1 1/4″ SCH 80 259.6288.5 317.3 346.2 375.0 403.9 432.7 461.6 1 1/2″ SCH 80 357.7 397.4437.1 476.9 516.6 556.4 596.1 635.9 1/2″ SCH 160 34.2 38.0 41.8 45.649.4 53.2 57.0 60.8 3/4″ SCH 160 59.5 66.2 72.8 79.4 86.0 92.6 99.2105.8 1″ SCH 160 105.6 117.3 129.1 140.8 152.5 164.2 176.0 187.7 1 1/4″SCH 160 213.9 237.7 261.4 285.2 309.0 332.7 356.5 380.3 1 1/2″ SCH 160284.6 316.2 347.8 379.4 411.1 442.7 474.3 505.9

TABLE 10 Drive Delta-P = (psi) 2500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 500′ 750′ 1000′ 1250′ 1500′1750′ 2000′ SIZE/SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 2.8 4.3 5.7 7.1 8.5 9.9 11.4 1/4″ SCH 40 5.2 7.810.4 13.0 15.6 18.2 20.8 3/8″ SCH 40 9.5 14.3 19.1 23.8 28.6 33.4 38.21/2″ SCH 40 15.2 22.8 30.4 38.0 45.6 53.1 60.7 3/4″ SCH 40 26.6 40.053.3 66.6 79.9 93.3 106.6 1″ SCH 40 43.2 64.8 86.4 108.0 129.6 151.2172.8 1 1/4″ SCH 40 74.7 112.1 149.5 186.9 224.2 261.6 299.0 1 1/2″ SCH40 101.7 152.6 203.5 254.3 305.2 356.1 407.0 1/8″ SCH 80 1.8 2.7 3.6 4.55.4 6.4 7.3 1/4″ SCH 80 3.6 5.4 7.2 8.9 10.7 12.5 14.3 3/8″ SCH 80 7.010.5 14.0 17.6 21.1 24.6 28.1 1/2″ SCH 80 11.7 17.6 23.4 29.3 35.1 41.046.8 3/4″ SCH 80 21.6 32.4 43.2 54.0 64.8 75.6 86.4 1″ SCH 80 35.9 53.971.9 89.9 107.8 125.8 143.8 1 1/4″ SCH 80 64.1 96.2 128.2 160.3 192.3224.4 256.4 1 1/2″ SCH 80 88.3 132.5 176.6 220.8 264.9 309.1 353.3 1/2″SCH 160 8.5 12.7 16.9 21.1 25.4 29.6 33.8 3/4″ SCH 160 14.7 22.1 29.436.8 44.1 51.5 58.8 1″ SCH 160 26.1 39.1 52.1 65.2 78.2 91.2 104.3 11/4″ SCH 160 52.8 79.2 105.6 132.0 158.4 184.9 211.3 1 1/2″ SCH 160 70.3105.4 140.5 175.7 210.8 245.9 281.1 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE 2250′ 2500′2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SIZE/SCHEDULE (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″SCH 40 12.8 14.2 15.6 17.0 18.5 19.9 21.3 22.7 1/4″ SCH 40 23.4 26.028.6 31.2 33.8 36.4 39.0 41.6 3/8″ SCH 40 42.9 47.7 52.5 57.2 62.0 66.871.5 76.3 1/2″ SCH 40 68.3 75.9 83.5 91.1 98.7 106.3 113.9 121.5 3/4″SCH 40 119.9 133.2 146.6 159.9 173.2 186.5 199.9 213.2 1″ SCH 40 194.4216.0 237.5 259.1 280.7 302.3 323.9 345.5 1 1/4″ SCH 40 336.4 373.7411.1 448.5 485.9 523.2 560.6 598.0 1 1/2″ SCH 40 457.8 508.7 559.6610.4 661.3 712.2 763.0 813.9 1/8″ SCH 80 8.2 9.1 10.0 10.9 11.8 12.713.6 14.5 1/4″ SCH 80 16.1 17.9 19.7 21.5 23.3 25.1 26.8 28.6 3/8″ SCH80 31.6 35.1 38.6 42.1 45.6 49.2 52.7 56.2 1/2″ SCH 80 52.7 58.5 64.470.2 76.1 81.9 87.8 93.6 3/4″ SCH 80 97.2 108.0 118.9 129.7 140.5 151.3162.1 172.9 1″ SCH 80 161.8 179.7 197.7 215.7 233.7 251.6 269.6 287.6 11/4″ SCH 80 288.5 320.5 352.6 384.6 416.7 448.7 480.8 512.9 1 1/2″ SCH80 397.4 441.6 485.7 529.9 574.0 618.2 662.3 706.5 1/2″ SCH 160 38.042.3 46.5 50.7 54.9 59.2 63.4 67.6 3/4″ SCH 160 66.2 73.5 80.9 88.2 95.6102.9 110.3 117.6 1″ SCH 160 117.3 130.4 143.4 156.4 169.5 182.5 195.5208.6 1 1/4″ SCH 160 237.7 264.1 290.5 316.9 343.3 369.7 396.1 422.5 11/2″ SCH 160 316.2 351.3 386.5 421.6 456.7 491.9 527.0 562.1

TABLE 11 DATA for oil Bulk Modulus = (psi) 250000 VOL. @ VOL. @ VOL. @VOL. @ OD ID WALL DEPTH DEPTH DEPTH DEPTH PIPE OD AREA ID AREA THCK 500750 1000 1250 SIZE/SCHEDULE (in) (in{circumflex over ( )}2) (in)(in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 0.405 0.129 0.269 0.057 0.068 340.8 511.2 681.6852.1 1/4″ SCH 40 0.540 0.229 0.364 0.104 0.088 624.1 936.1 1248.11560.1 3/8″ SCH 40 0.675 0.358 0.493 0.191 0.091 1144.8 1717.1 2289.52861.9 1/2″ SCH 40 0.840 0.554 0.622 0.304 0.109 1822.2 2733.3 3644.44555.6 3/4″ SCH 40 1.050 0.865 0.824 0.533 0.113 3198.0 4797.0 6396.07994.9 1″ SCH 40 1.315 1.357 1.049 0.864 0.133 5182.9 7774.3 10365.812957.2 1 1/4″ SCH 40 1.660 2.163 1.380 1.495 0.140 8969.7 13454.617939.4 22424.3 1 1/2″ SCH 40 1.900 2.834 1.610 2.035 0.145 12208.818313.2 24417.6 30522.0 1/8″ SCH 80 0.405 0.129 0.215 0.036 0.095 217.7326.6 435.4 544.3 1/4″ SCH 80 0.540 0.229 0.302 0.072 0.119 429.6 644.4859.1 1073.9 3/8″ SCH 80 0.675 0.358 0.423 0.140 0.126 842.8 1264.11685.5 2106.9 1/2″ SCH 80 0.840 0.554 0.546 0.234 0.147 1404.1 2106.22808.3 3510.3 3/4″ SCH 80 1.050 0.865 0.742 0.432 0.154 2593.2 3889.75186.3 6482.9 1″ SCH 80 1.315 1.357 0.957 0.719 0.179 4313.6 6470.58627.3 10784.1 1 1/4″ SCH 80 1.660 2.163 1.278 1.282 0.191 7692.811539.2 15385.5 19231.9 1 1/2″ SCH 80 1.900 2.834 1.500 1.766 0.20010597.5 15896.3 21195.0 26493.8 1/2″ SCH 160 0.840 0.554 0.464 0.1690.188 1014.0 1521.1 2028.1 2535.1 3/4″ SCH 160 1.050 0.865 0.612 0.2940.219 1764.1 2646.2 3528.2 4410.3 1″ SCH 160 1.315 1.357 0.815 0.5210.250 3128.5 4692.7 6257.0 7821.2 1 1/4″ SCH 160 1.660 2.163 1.160 1.0560.250 6337.8 9506.7 12675.6 15844.4 1 1/2″ SCH 160 1.900 2.834 1.3381.405 0.281 8432.0 12648.1 16864.1 21080.1 VOL. @ VOL. @ VOL. @ VOL. @OD ID WALL DEPTH DEPTH DEPTH DEPTH PIPE OD AREA ID AREA THCK 1500 17502000 2250 SIZE/SCHEDULE (in) (in{circumflex over ( )}2) (in)(in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 0.405 0.129 0.269 0.057 0.068 1022.5 1192.91363.3 1533.7 1/4″ SCH 40 0.540 0.229 0.364 0.104 0.088 1872.2 2184.22496.2 2808.3 3/8″ SCH 40 0.675 0.358 0.493 0.191 0.091 3434.3 4006.74579.0 5151.4 1/2″ SCH 40 0.840 0.554 0.622 0.304 0.109 5466.7 6377.87288.9 8200.0 3/4″ SCH 40 1.050 0.865 0.824 0.533 0.113 9593.9 11192.912791.9 14390.9 1″ SCH 40 1.315 1.357 1.049 0.864 0.133 15548.7 18140.120731.6 23323.0 1 1/4″ SCH 40 1.660 2.163 1.380 1.495 0.140 26909.231394.0 35878.9 40363.8 1 1/2″ SCH 40 1.900 2.834 1.610 2.035 0.14536626.4 42730.8 48835.2 54939.6 1/8″ SCH 80 0.405 0.129 0.215 0.0360.095 653.2 762.0 870.9 979.7 1/4″ SCH 80 0.540 0.229 0.302 0.072 0.1191288.7 1503.5 1718.3 1933.1 3/8″ SCH 80 0.675 0.358 0.423 0.140 0.1262528.3 2949.6 3371.0 3792.4 1/2″ SCH 80 0.840 0.554 0.546 0.234 0.1474212.4 4914.4 5616.5 6318.6 3/4″ SCH 80 1.050 0.865 0.742 0.432 0.1547779.5 9076.0 10372.6 11669.2 1″ SCH 80 1.315 1.357 0.957 0.719 0.17912940.9 15097.8 17254.6 19411.4 1 1/4″ SCH 80 1.660 2.163 1.278 1.2820.191 23078.3 26924.7 30771.1 34617.5 1 1/2″ SCH 80 1.900 2.834 1.5001.766 0.200 31792.5 37091.3 42390.0 47688.8 1/2″ SCH 160 0.840 0.5540.464 0.169 0.188 3042.1 3549.2 4056.2 4563.2 3/4″ SCH 160 1.050 0.8650.612 0.294 0.219 5292.3 6174.4 7056.4 7938.5 1″ SCH 160 1.315 1.3570.815 0.521 0.250 9385.5 10949.7 12514.0 14078.2 1 1/4″ SCH 160 1.6602.163 1.160 1.056 0.250 19013.3 22182.2 25351.1 28520.0 1 1/2″ SCH 1601.900 2.834 1.338 1.405 0.281 25296.1 29512.2 33728.2 37944.2 VOL. @VOL. @ VOL. @ VOL. @ OD ID WALL DEPTH DEPTH DEPTH DEPTH PIPE OD AREA IDAREA THCK 2500 2750 3000 3250 SIZE/SCHEDULE (in) (in{circumflex over( )}2) (in) (in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) 1/8″ SCH 40 0.405 0.129 0.269 0.057 0.068 1704.1 1874.52044.9 2215.3 1/4″ SCH 40 0.540 0.229 0.364 0.104 0.088 3120.3 3432.33744.3 4056.4 3/8″ SCH 40 0.675 0.358 0.493 0.191 0.091 5723.8 6296.26868.6 7440.9 1/2″ SCH 40 0.840 0.554 0.622 0.304 0.109 9111.1 10022.210933.3 11844.5 3/4″ SCH 40 1.050 0.865 0.824 0.533 0.113 15989.917588.9 19187.9 20786.9 1″ SCH 40 1.315 1.357 1.049 0.864 0.133 25914.428505.9 31097.3 33688.8 1 1/4″ SCH 40 1.660 2.163 1.380 1.495 0.14044848.6 49333.5 53818.3 58303.2 1 1/2″ SCH 40 1.900 2.834 1.610 2.0350.145 61044.0 67148.4 73252.7 79357.1 1/8″ SCH 80 0.405 0.129 0.2150.036 0.095 1088.6 1197.5 1306.3 1415.2 1/4″ SCH 80 0.540 0.229 0.3020.072 0.119 2147.9 2362.6 2577.4 2792.2 3/8″ SCH 80 0.675 0.358 0.4230.140 0.126 4213.8 4635.2 5056.5 5477.9 1/2″ SCH 80 0.840 0.554 0.5460.234 0.147 7020.6 7722.7 8424.8 9126.8 3/4″ SCH 80 1.050 0.865 0.7420.432 0.154 12965.8 14262.4 15558.9 16855.5 1″ SCH 80 1.315 1.357 0.9570.719 0.179 21568.2 23725.1 25881.9 28038.7 1 1/4″ SCH 80 1.660 2.1631.278 1.282 0.191 38463.8 42310.2 46156.6 50003.0 1 1/2″ SCH 80 1.9002.834 1.500 1.766 0.200 52987.5 58286.3 63585.0 68883.8 1/2″ SCH 1600.840 0.554 0.464 0.169 0.188 5070.2 5577.2 6084.3 6591.3 3/4″ SCH 1601.050 0.865 0.612 0.294 0.219 8820.5 9702.6 10584.6 11466.7 1″ SCH 1601.315 1.357 0.815 0.521 0.250 15642.5 17206.7 18771.0 20335.2 1 1/4″ SCH160 1.660 2.163 1.160 1.056 0.250 31688.9 34857.8 38026.7 41195.5 1 1/2″SCH 160 1.900 2.834 1.338 1.405 0.281 42160.2 46376.3 50592.3 54808.3VOL. @ VOL. @ VOL. @ OD ID WALL DEPTH DEPTH DEPTH PIPE OD AREA ID AREATHCK 3500 3750 4000 SIZE/SCHEDULE (in) (in{circumflex over ( )}2) (in)(in{circumflex over ( )}2) (in) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) 1/8″ SCH 40 0.4050.129 0.269 0.057 0.068 2385.7 2556.2 2726.6 1/4″ SCH 40 0.540 0.2290.364 0.104 0.088 4368.4 4680.4 4992.4 3/8″ SCH 40 0.675 0.358 0.4930.191 0.091 8013.3 8585.7 9158.1 1/2″ SCH 40 0.840 0.554 0.622 0.3040.109 12755.6 13666.7 14577.8 3/4″ SCH 40 1.050 0.865 0.824 0.533 0.11322385.8 23984.8 25583.8 1″ SCH 40 1.315 1.357 1.049 0.864 0.133 36280.238871.7 41463.1 1 1/4″ SCH 40 1.660 2.163 1.380 1.495 0.140 62788.167272.9 71757.8 1 1/2″ SCH 40 1.900 2.834 1.610 2.035 0.145 85461.591565.9 97670.3 1/8″ SCH 80 0.405 0.129 0.215 0.036 0.095 1524.0 1632.91741.8 1/4″ SCH 80 0.540 0.229 0.302 0.072 0.119 3007.0 3221.8 3436.63/8″ SCH 80 0.675 0.358 0.423 0.140 0.126 5899.3 6320.7 6742.0 1/2″ SCH80 0.840 0.554 0.546 0.234 0.147 9828.9 10530.9 11233.0 3/4″ SCH 801.050 0.865 0.742 0.432 0.154 18152.1 19448.7 20745.3 1″ SCH 80 1.3151.357 0.957 0.719 0.179 30195.5 32352.4 34509.2 1 1/4″ SCH 80 1.6602.163 1.278 1.282 0.191 53849.4 57695.8 61542.1 1 1/2″ SCH 80 1.9002.834 1.500 1.766 0.200 74182.5 79481.3 84780.0 1/2″ SCH 160 0.840 0.5540.464 0.169 0.188 7098.3 7605.3 8112.4 3/4″ SCH 160 1.050 0.865 0.6120.294 0.219 12348.7 13230.8 14112.8 1″ SCH 160 1.315 1.357 0.815 0.5210.250 21899.5 23463.7 25028.0 1 1/4″ SCH 160 1.660 2.163 1.160 1.0560.250 44364.4 47533.3 50702.2 1 1/2″ SCH 160 1.900 2.834 1.338 1.4050.281 59024.3 63240.4 67456.4

TABLE 12 Drive Delta-P = (psi) 500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 0.7 1.01.4 1.7 2.0 2.4 2.7 3.1 ¼″ SCH 40 1.2 1.9 2.5 3.1 3.7 4.4 5.0 5.6 ⅜″ SCH40 2.3 3.4 4.6 5.7 6.9 8.0 9.2 10.3 ½″ SCH 40 3.6 5.5 7.3 9.1 10.9 12.814.6 16.4 ¾″ SCH 40 6.4 9.6 12.8 16.0 19.2 22.4 25.6 28.8 1″ SCH 40 10.415.5 20.7 25.9 31.1 36.3 41.5 46.6 1 ¼″ SCH 40 17.9 26.9 35.9 44.8 53.862.8 71.8 80.7 1 ½″ SCH 40 24.4 36.6 48.8 61.0 73.3 85.5 97.7 109.9 ⅛″SCH 80 0.4 0.7 0.9 1.1 1.3 1.5 1.7 2.0 ¼″ SCH 80 0.9 1.3 1.7 2.1 2.6 3.03.4 3.9 ⅜″ SCH 80 1.7 2.5 3.4 4.2 5.1 5.9 6.7 7.6 ½″ SCH 80 2.8 4.2 5.67.0 8.4 9.8 11.2 12.6 ¾″ SCH 80 5.2 7.8 10.4 13.0 15.6 18.2 20.7 23.3 1″SCH 80 8.6 12.9 17.3 21.6 25.9 30.2 34.5 38.8 1 ¼″ SCH 80 15.4 23.1 30.838.5 46.2 53.8 61.5 69.2 1 ½″ SCH 80 21.2 31.8 42.4 53.0 63.6 74.2 84.895.4 ½″ SCH 160 2.0 3.0 4.1 5.1 6.1 7.1 8.1 9.1 ¾″ SCH 160 3.5 5.3 7.18.8 10.6 12.3 14.1 15.9 1″ SCH 160 6.3 9.4 12.5 15.6 18.8 21.9 25.0 28.21 ¼″ SCH 160 12.7 19.0 25.4 31.7 38.0 44.4 50.7 57.0 1 ½″ SCH 160 16.925.3 33.7 42.2 50.6 59.0 67.5 75.9 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′3500′ 3750′ 4000′ SCHEDULE (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) ⅛″ SCH 40 3.4 3.7 4.1 4.4 4.8 5.1 5.5 ¼″ SCH 40 6.2 6.9 7.58.1 8.7 9.4 10.0 ⅜″ SCH 40 11.4 12.6 13.7 14.9 16.0 17.2 18.3 ½″ SCH 4018.2 20.0 21.9 23.7 25.5 27.3 29.2 ¾″ SCH 40 32.0 35.2 38.4 41.6 44.848.0 51.2 1″ SCH 40 51.8 57.0 62.2 67.4 72.6 77.7 82.9 1 ¼″ SCH 40 89.798.7 107.6 116.6 125.6 134.5 143.5 1 ½″ SCH 40 122.1 134.3 146.5 158.7170.9 183.1 195.3 ⅛″ SCH 80 2.2 2.4 2.6 2.8 3.0 3.3 3.5 ¼″ SCH 80 4.34.7 5.2 5.6 6.0 6.4 6.9 ⅜″ SCH 80 8.4 9.3 10.1 11.0 11.8 12.6 13.5 ½″SCH 80 14.0 15.4 16.8 18.3 19.7 21.1 22.5 ¾″ SCH 80 25.9 28.5 31.1 33.736.3 38.9 41.5 1″ SCH 80 43.1 47.5 51.8 56.1 60.4 64.7 69.0 1 ¼″ SCH 8076.9 84.6 92.3 100.0 107.7 115.4 123.1 1 ½″ SCH 80 106.0 116.6 127.2137.8 148.4 159.0 169.6 ½″ SCH 160 10.1 11.2 12.2 13.2 14.2 15.2 16.2 ¾″SCH 160 17.6 19.4 21.2 22.9 24.7 26.5 28.2 1″ SCH 160 31.3 34.4 37.540.7 43.8 46.9 50.1 1 ¼″ SCH 160 63.4 69.7 76.1 82.4 88.7 95.1 101.4 1½″ SCH 160 84.3 92.8 101.2 109.6 118.0 126.5 134.9

TABLE 13 Drive Delta-P = (psi) 750 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 1.0 1.52.0 2.6 3.1 3.6 4.1 4.6 ¼″ SCH 40 1.9 2.8 3.7 4.7 5.6 6.6 7.5 8.4 ⅜″ SCH40 3.4 5.2 6.9 8.6 10.3 12.0 13.7 15.5 ½″ SCH 40 5.5 8.2 10.9 13.7 16.419.1 21.9 24.6 ¾″ SCH 40 9.6 14.4 19.2 24.0 28.8 33.6 38.4 43.2 1″ SCH40 15.5 23.3 31.1 38.9 46.6 54.4 62.2 70.0 1 ¼″ SCH 40 26.9 40.4 53.867.3 80.7 94.2 107.6 121.1 1 ½″ SCH 40 36.6 54.9 73.3 91.6 109.9 128.2146.5 164.8 ⅛″ SCH 80 0.7 1.0 1.3 1.6 2.0 2.3 2.6 2.9 ¼″ SCH 80 1.3 1.92.6 3.2 3.9 4.5 5.2 5.8 ⅜″ SCH 80 2.5 3.8 5.1 6.3 7.6 8.8 10.1 11.4 ½″SCH 80 4.2 6.3 8.4 10.5 12.6 14.7 16.8 19.0 ¾″ SCH 80 7.8 11.7 15.6 19.423.3 27.2 31.1 35.0 1″ SCH 80 12.9 19.4 25.9 32.4 38.8 45.3 51.8 58.2 1¼″ SCH 80 23.1 34.6 46.2 57.7 69.2 80.8 92.3 103.9 1 ½″ SCH 80 31.8 47.763.6 79.5 95.4 111.3 127.2 143.1 ½″ SCH 160 3.0 4.6 6.1 7.6 9.1 10.612.2 13.7 ¾″ SCH 160 5.3 7.9 10.6 13.2 15.9 18.5 21.2 23.8 1″ SCH 1609.4 14.1 18.8 23.5 28.2 32.8 37.5 42.2 1 ¼″ SCH 160 19.0 28.5 38.0 47.557.0 66.5 76.1 85.6 1 ½″ SCH 160 25.3 37.9 50.6 63.2 75.9 88.5 101.2113.8 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SCHEDULE(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 5.1 5.66.1 6.6 7.2 7.7 8.2 ¼″ SCH 40 9.4 10.3 11.2 12.2 13.1 14.0 15.0 ⅜″ SCH40 17.2 18.9 20.6 22.3 24.0 25.8 27.5 ½″ SCH 40 27.3 30.1 32.8 35.5 38.341.0 43.7 ¾″ SCH 40 48.0 52.8 57.6 62.4 67.2 72.0 76.8 1″ SCH 40 77.785.5 93.3 101.1 108.8 116.6 124.4 1 ¼″ SCH 40 134.5 148.0 161.5 174.9188.4 201.8 215.3 1 1/2″ SCH 40 183.1 201.4 219.8 238.1 256.4 274.7293.0 ⅛″ SCH 80 3.3 3.6 3.9 4.2 4.6 4.9 5.2 ¼″ SCH 80 6.4 7.1 7.7 8.49.0 9.7 10.3 ⅜″ SCH 80 12.6 13.9 15.2 16.4 17.7 19.0 20.2 ½″ SCH 80 21.123.2 25.3 27.4 29.5 31.6 33.7 ¾″ SCH 80 38.9 42.8 46.7 50.6 54.5 58.362.2 1″ SCH 80 64.7 71.2 77.6 84.1 90.6 97.1 103.5 1 ¼″ SCH 80 115.4126.9 138.5 150.0 161.5 173.1 184.6 1 ½″ SCH 80 159.0 174.9 190.8 206.7222.5 238.4 254.3 ½″ SCH 160 15.2 16.7 18.3 19.8 21.3 22.8 24.3 ¾″ SCH160 26.5 29.1 31.8 34.4 37.0 39.7 42.3 1″ SCH 160 46.9 51.6 56.3 61.065.7 70.4 75.1 1 ¼″ SCH 160 95.1 104.6 114.1 123.6 133.1 142.6 152.1 1½″ SCH 160 126.5 139.1 151.8 164.4 177.1 189.7 202.4

TABLE 14 Drive Delta-P = (psi) 1000 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 1.4 2.02.7 3.4 4.1 4.8 5.5 6.1 ¼″ SCH 40 2.5 3.7 5.0 6.2 7.5 8.7 10.0 11.2 ⅜″SCH 40 4.6 6.9 9.2 11.4 13.7 16.0 18.3 20.6 ½″ SCH 40 7.3 10.9 14.6 18.221.9 25.5 29.2 32.8 ¾″ SCH 40 12.8 19.2 25.6 32.0 38.4 44.8 51.2 57.6 1″SCH 40 20.7 31.1 41.5 51.8 62.2 72.6 82.9 93.3 1 ¼″ SCH 40 35.9 53.871.8 89.7 107.6 125.6 143.5 161.5 1 ½″ SCH 40 48.8 73.3 97.7 122.1 146.5170.9 195.3 219.8 ⅛″ SCH 80 0.9 1.3 1.7 2.2 2.6 3.0 3.5 3.9 ¼″ SCH 801.7 2.6 3.4 4.3 5.2 6.0 6.9 7.7 ⅜″ SCH 80 3.4 5.1 6.7 8.4 10.1 11.8 13.515.2 ½″ SCH 80 5.6 8.4 11.2 14.0 16.8 19.7 22.5 25.3 ¾″ SCH 80 10.4 15.620.7 25.9 31.1 36.3 41.5 46.7 1″ SCH 80 17.3 25.9 34.5 43.1 51.8 60.469.0 77.6 1 ¼″ SCH 80 30.8 46.2 61.5 76.9 92.3 107.7 123.1 138.5 1 ½″SCH 80 42.4 63.6 84.8 106.0 127.2 148.4 169.6 190.8 ½″ SCH 160 4.1 6.18.1 10.1 12.2 14.2 16.2 18.3 ¾″ SCH 160 7.1 10.6 14.1 17.6 21.2 24.728.2 31.8 1″ SCH 160 12.5 18.8 25.0 31.3 37.5 43.8 50.1 56.3 1 ¼″ SCH160 25.4 38.0 50.7 63.4 76.1 88.7 101.4 114.1 1 ½″ SCH 160 33.7 50.667.5 84.3 101.2 118.0 134.9 151.8 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′3500′ 3750′ 4000′ SCHEDULE (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) ⅛″ SCH 40 6.8 7.5 8.2 8.9 9.5 10.2 10.9 ¼″ SCH 40 12.5 13.715.0 16.2 17.5 18.7 20.0 ⅜″ SCH 40 22.9 25.2 27.5 29.8 32.1 34.3 36.6 ½″SCH 40 36.4 40.1 43.7 47.4 51.0 54.7 58.3 ¾″ SCH 40 64.0 70.4 76.8 83.189.5 95.9 102.3 1″ SCH 40 103.7 114.0 124.4 134.8 145.1 155.5 165.9 1 ¼″SCH 40 179.4 197.3 215.3 233.2 251.2 269.1 287.0 1 ½″ SCH 40 244.2 268.6293.0 317.4 341.8 366.3 390.7 ⅛″ SCH 80 4.4 4.8 5.2 5.7 6.1 6.5 7.0 ¼″SCH 80 8.6 9.5 10.3 11.2 12.0 12.9 13.7 ⅜″ SCH 80 16.9 18.5 20.2 21.923.6 25.3 27.0 ½″ SCH 80 28.1 30.9 33.7 36.5 39.3 42.1 44.9 ¾″ SCH 8051.9 57.0 62.2 67.4 72.6 77.8 83.0 1″ SCH 80 86.3 94.9 103.5 112.2 120.8129.4 138.0 1 ¼″ SCH 80 153.9 169.2 184.6 200.0 215.4 230.8 246.2 1 ½″SCH 80 212.0 233.1 254.3 275.5 296.7 317.9 339.1 ½″ SCH 160 20.3 22.324.3 26.4 28.4 30.4 32.4 ¾″ SCH 160 35.3 38.8 42.3 45.9 49.4 52.9 56.51″ SCH 160 62.6 68.8 75.1 81.3 87.6 93.9 100.1 1 ¼″ SCH 160 126.8 139.4152.1 164.8 177.5 190.1 202.8 1 ½″ SCH 160 168.6 185.5 202.4 219.2 236.1253.0 269.8

TABLE 15 Drive Delta-P = (psi) 1250 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 1.7 2.63.4 4.3 5.1 6.0 6.8 7.7 ¼″ SCH 40 3.1 4.7 6.2 7.8 9.4 10.9 12.5 14.0 ⅜″SCH 40 5.7 8.6 11.4 14.3 17.2 20.0 22.9 25.8 ½″ SCH 40 9.1 13.7 18.222.8 27.3 31.9 36.4 41.0 ¾″ SCH 40 16.0 24.0 32.0 40.0 48.0 56.0 64.072.0 1″ SCH 40 25.9 38.9 51.8 64.8 77.7 90.7 103.7 116.6 1 ¼″ SCH 4044.8 67.3 89.7 112.1 134.5 157.0 179.4 201.8 1 ½″ SCH 40 61.0 91.6 122.1152.6 183.1 213.7 244.2 274.7 ⅛″ SCH 80 1.1 1.6 2.2 2.7 3.3 3.8 4.4 4.9¼″ SCH 80 2.1 3.2 4.3 5.4 6.4 7.5 8.6 9.7 ⅜″ SCH 80 4.2 6.3 8.4 10.512.6 14.7 16.9 19.0 ½″ SCH 80 7.0 10.5 14.0 17.6 21.1 24.6 28.1 31.6 ¾″SCH 80 13.0 19.4 25.9 32.4 38.9 45.4 51.9 58.3 1″ SCH 80 21.6 32.4 43.153.9 64.7 75.5 86.3 97.1 1 ¼″ SCH 80 38.5 57.7 76.9 96.2 115.4 134.6153.9 173.1 1 ½″ SCH 80 53.0 79.5 106.0 132.5 159.0 185.5 212.0 238.4 ½″SCH 160 5.1 7.6 10.1 12.7 15.2 17.7 20.3 22.8 ¾″ SCH 160 8.8 13.2 17.622.1 26.5 30.9 35.3 39.7 1″ SCH 160 15.6 23.5 31.3 39.1 46.9 54.7 62.670.4 1 ¼″ SCH 160 31.7 47.5 63.4 79.2 95.1 110.9 126.8 142.6 1 ½″ SCH160 42.2 63.2 84.3 105.4 126.5 147.6 168.6 189.7 DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′3250′ 3500′ 3750′ 4000′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) ⅛″ SCH 40 8.5 9.4 10.2 11.1 11.9 12.8 13.6 ¼″SCH 40 15.6 17.2 18.7 20.3 21.8 23.4 25.0 ⅜″ SCH 40 28.6 31.5 34.3 37.240.1 42.9 45.8 ½″ SCH 40 45.6 50.1 54.7 59.2 63.8 68.3 72.9 ¾″ SCH 4079.9 87.9 95.9 103.9 111.9 119.9 127.9 1″ SCH 40 129.6 142.5 155.5 168.4181.4 194.4 207.3 1 ¼″ SCH 40 224.2 246.7 269.1 291.5 313.9 336.4 358.81 ½″ SCH 40 305.2 335.7 366.3 396.8 427.3 457.8 488.4 ⅛″ SCH 80 5.4 6.06.5 7.1 7.6 8.2 8.7 ¼″ SCH 80 10.7 11.8 12.9 14.0 15.0 16.1 17.2 ⅜″ SCH80 21.1 23.2 25.3 27.4 29.5 31.6 33.7 ½″ SCH 80 35.1 38.6 42.1 45.6 49.152.7 56.2 ¾″ SCH 80 64.8 71.3 77.8 84.3 90.8 97.2 103.7 1″ SCH 80 107.8118.6 129.4 140.2 151.0 161.8 172.5 1 ¼″ SCH 80 192.3 211.6 230.8 250.0269.2 288.5 307.7 1 ½″ SCH 80 264.9 291.4 317.9 344.4 370.9 397.4 423.9½″ SCH 160 25.4 27.9 30.4 33.0 35.5 38.0 40.6 ¾″ SCH 160 44.1 48.5 52.957.3 61.7 66.2 70.6 1″ SCH 160 78.2 86.0 93.9 101.7 109.5 117.3 125.1 1¼″ SCH 160 158.4 174.3 190.1 206.0 221.8 237.7 253.5 1 ½″ SCH 160 210.8231.9 253.0 274.0 295.1 316.2 337.3

TABLE 16 Drive Delta-P = (psi) 1500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 2.0 3.14.1 5.1 6.1 7.2 8.2 9.2 ¼″ SCH 40 3.7 5.6 7.5 9.4 11.2 13.1 15.0 16.8 ⅜″SCH 40 6.9 10.3 13.7 17.2 20.6 24.0 27.5 30.9 ½″ SCH 40 10.9 16.4 21.927.3 32.8 38.3 43.7 49.2 ¾″ SCH 40 19.2 28.8 38.4 48.0 57.6 67.2 76.886.3 1″ SCH 40 31.1 46.6 62.2 77.7 93.3 108.8 124.4 139.9 1 ¼″ SCH 4053.8 80.7 107.6 134.5 161.5 188.4 215.3 242.2 1 ½″ SCH 40 73.3 109.9146.5 183.1 219.8 256.4 293.0 329.6 ⅛″ SCH 80 1.3 2.0 2.6 3.3 3.9 4.65.2 5.9 ¼″ SCH 80 2.6 3.9 5.2 6.4 7.7 9.0 10.3 11.6 ⅜″ SCH 80 5.1 7.610.1 12.6 15.2 17.7 20.2 22.8 ½″ SCH 80 8.4 12.6 16.8 21.1 25.3 29.533.7 37.9 ¾″ SCH 80 15.6 23.3 31.1 38.9 46.7 54.5 62.2 70.0 1″ SCH 8025.9 38.8 51.8 64.7 77.6 90.6 103.5 116.5 1 ¼″ SCH 80 46.2 69.2 92.3115.4 138.5 161.5 184.6 207.7 1 ½″ SCH 80 63.6 95.4 127.2 159.0 190.8222.5 254.3 286.1 ½″ SCH 160 6.1 9.1 12.2 15.2 18.3 21.3 24.3 27.4 ¾″SCH 160 10.6 15.9 21.2 26.5 31.8 37.0 42.3 47.6 1″ SCH 160 18.8 28.237.5 46.9 56.3 65.7 75.1 84.5 1 ¼″ SCH 160 38.0 57.0 76.1 95.1 114.1133.1 152.1 171.1 1 ½″ SCH 160 50.6 75.9 101.2 126.5 151.8 177.1 202.4227.7 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SCHEDULE(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 10.211.2 12.3 13.3 14.3 15.3 16.4 ¼″ SCH 40 18.7 20.6 22.5 24.3 26.2 28.130.0 ⅜″ SCH 40 34.3 37.8 41.2 44.6 48.1 51.5 54.9 ½″ SCH 40 54.7 60.165.6 71.1 76.5 82.0 87.5 ¾″ SCH 40 95.9 105.5 115.1 124.7 134.3 143.9153.5 1″ SCH 40 155.5 171.0 186.6 202.1 217.7 233.2 248.8 1 ¼″ SCH 40269.1 296.0 322.9 349.8 376.7 403.6 430.5 1 ½″ SCH 40 366.3 402.9 439.5476.1 512.8 549.4 586.0 ⅛″ SCH 80 6.5 7.2 7.8 8.5 9.1 9.8 10.5 ¼″ SCH 8012.9 14.2 15.5 16.8 18.0 19.3 20.6 ⅜″ SCH 80 25.3 27.8 30.3 32.9 35.437.9 40.5 ½″ SCH 80 42.1 46.3 50.5 54.8 59.0 63.2 67.4 ¾″ SCH 80 77.885.6 93.4 101.1 108.9 116.7 124.5 1″ SCH 80 129.4 142.4 155.3 168.2181.2 194.1 207.1 1 ¼″ SCH 80 230.8 253.9 276.9 300.0 323.1 346.2 369.31 ½″ SCH 80 317.9 349.7 381.5 413.3 445.1 476.9 508.7 ½″ SCH 160 30.433.5 36.5 39.5 42.6 45.6 48.7 ¾″ SCH 160 52.9 58.2 63.5 68.8 74.1 79.484.7 1″ SCH 160 93.9 103.2 112.6 122.0 131.4 140.8 150.2 1 ¼″ SCH 160190.1 209.1 228.2 247.2 266.2 285.2 304.2 1 ½″ SCH 160 253.0 278.3 303.6328.8 354.1 379.4 404.7

TABLE 17 Drive Delta-P = (psi) 1750 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 2.4 3.64.8 6.0 7.2 8.4 9.5 10.7 ¼″ SCH 40 4.4 6.6 8.7 10.9 13.1 15.3 17.5 19.7⅜″ SCH 40 8.0 12.0 16.0 20.0 24.0 28.0 32.1 36.1 ½″ SCH 40 12.8 19.125.5 31.9 38.3 44.6 51.0 57.4 ¾″ SCH 40 22.4 33.6 44.8 56.0 67.2 78.489.5 100.7 1″ SCH 40 36.3 54.4 72.6 90.7 108.8 127.0 145.1 163.3 1 ¼″SCH 40 62.8 94.2 125.6 157.0 188.4 219.8 251.2 282.5 1 ½″ SCH 40 85.5128.2 170.9 213.7 256.4 299.1 341.8 384.6 ⅛″ SCH 80 1.5 2.3 3.0 3.8 4.65.3 6.1 6.9 ¼″ SCH 80 3.0 4.5 6.0 7.5 9.0 10.5 12.0 13.5 ⅜″ SCH 80 5.98.8 11.8 14.7 17.7 20.6 23.6 26.5 ½″ SCH 80 9.8 14.7 19.7 24.6 29.5 34.439.3 44.2 ¾″ SCH 80 18.2 27.2 36.3 45.4 54.5 63.5 72.6 81.7 1″ SCH 8030.2 45.3 60.4 75.5 90.6 105.7 120.8 135.9 1 ¼″ SCH 80 53.8 80.8 107.7134.6 161.5 188.5 215.4 242.3 1 ½″ SCH 80 74.2 111.3 148.4 185.5 222.5259.6 296.7 333.8 ½″ SCH 160 7.1 10.6 14.2 17.7 21.3 24.8 28.4 31.9 ¾″SCH 160 12.3 18.5 24.7 30.9 37.0 43.2 49.4 55.6 1″ SCH 160 21.9 32.843.8 54.7 65.7 76.6 87.6 98.5 1 ¼″ SCH 160 44.4 66.5 88.7 110.9 133.1155.3 177.5 199.6 1 ½″ SCH 160 59.0 88.5 118.0 147.6 177.1 206.6 236.1265.6 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′ SCHEDULE(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 11.913.1 14.3 15.5 16.7 17.9 19.1 ¼″ SCH 40 21.8 24.0 26.2 28.4 30.6 32.834.9 ⅜″ SCH 40 40.1 44.1 48.1 52.1 56.1 60.1 64.1 ½″ SCH 40 63.8 70.276.5 82.9 89.3 95.7 102.0 ¾″ SCH 40 111.9 123.1 134.3 145.5 156.7 167.9179.1 1″ SCH 40 181.4 199.5 217.7 235.8 254.0 272.1 290.2 1 ¼″ SCH 40313.9 345.3 376.7 408.1 439.5 470.9 502.3 1 ½″ SCH 40 427.3 470.0 512.8555.5 598.2 641.0 683.7 ⅛″ SCH 80 7.6 8.4 9.1 9.9 10.7 11.4 12.2 ¼″ SCH80 15.0 16.5 18.0 19.5 21.0 22.6 24.1 ⅜″ SCH 80 29.5 32.4 35.4 38.3 41.344.2 47.2 ½″ SCH 80 49.1 54.1 59.0 63.9 68.8 73.7 78.6 ¾″ SCH 80 90.899.8 108.9 118.0 127.1 136.1 145.2 1″ SCH 80 151.0 166.1 181.2 196.3211.4 226.5 241.6 1 ¼″ SCH 80 269.2 296.2 323.1 350.0 376.9 403.9 430.81 ½″ SCH 80 370.9 408.0 445.1 482.2 519.3 556.4 593.5 ½″ SCH 160 35.539.0 42.6 46.1 49.7 53.2 56.8 ¾″ SCH 160 61.7 67.9 74.1 80.3 86.4 92.698.8 1″ SCH 160 109.5 120.4 131.4 142.3 153.3 164.2 175.2 1 ¼″ SCH 160221.8 244.0 266.2 288.4 310.6 332.7 354.9 1 ½″ SCH 160 295.1 324.6 354.1383.7 413.2 442.7 472.2

TABLE 18 Drive Delta-P = (psi) 2000 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 2.7 4.15.5 6.8 8.2 9.5 10.9 12.3 ¼″ SCH 40 5.0 7.5 10.0 12.5 15.0 17.5 20.022.5 ⅜″ SCH 40 9.2 13.7 18.3 22.9 27.5 32.1 36.6 41.2 ½″ SCH 40 14.621.9 29.2 36.4 43.7 51.0 58.3 65.6 ¾″ SCH 40 25.6 38.4 51.2 64.0 76.889.5 102.3 115.1 1″ SCH 40 41.5 62.2 82.9 103.7 124.4 145.1 165.9 186.61 ¼″ SCH 40 71.8 107.6 143.5 179.4 215.3 251.2 287.0 322.9 1 ½″ SCH 4097.7 146.5 195.3 244.2 293.0 341.8 390.7 439.5 ⅛″ SCH 80 1.7 2.6 3.5 4.45.2 6.1 7.0 7.8 ¼″ SCH 80 3.4 5.2 6.9 8.6 10.3 12.0 13.7 15.5 ⅜″ SCH 806.7 10.1 13.5 16.9 20.2 23.6 27.0 30.3 ½″ SCH 80 11.2 16.8 22.5 28.133.7 39.3 44.9 50.5 ¾″ SCH 80 20.7 31.1 41.5 51.9 62.2 72.6 83.0 93.4 1″SCH 80 34.5 51.8 69.0 86.3 103.5 120.8 138.0 155.3 1 ¼″ SCH 80 61.5 92.3123.1 153.9 184.6 215.4 246.2 276.9 1 ½″ SCH 80 84.8 127.2 169.6 212.0254.3 296.7 339.1 381.5 ½″ SCH 160 8.1 12.2 16.2 20.3 24.3 28.4 32.436.5 ¾″ SCH 160 14.1 21.2 28.2 35.3 42.3 49.4 56.5 63.5 1″ SCH 160 25.037.5 50.1 62.6 75.1 87.6 100.1 112.6 1 ¼″ SCH 160 50.7 76.1 101.4 126.8152.1 177.5 202.8 228.2 1 ½″ SCH 160 67.5 101.2 134.9 168.6 202.4 236.1269.8 303.6 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUME VOLUMEVOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @ LOSS @LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′ 4000′SCHEDULE (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH40 13.6 15.0 16.4 17.7 19.1 20.4 21.8 ¼″ SCH 40 25.0 27.5 30.0 32.5 34.937.4 39.9 ⅜″ SCH 40 45.8 50.4 54.9 59.5 64.1 68.7 73.3 ½″ SCH 40 72.980.2 87.5 94.8 102.0 109.3 116.6 ¾″ SCH 40 127.9 140.7 153.5 166.3 179.1191.9 204.7 1″ SCH 40 207.3 228.0 248.8 269.5 290.2 311.0 331.7 1 ¼″ SCH40 358.8 394.7 430.5 466.4 502.3 538.2 574.1 1 ½″ SCH 40 488.4 537.2586.0 634.9 683.7 732.5 781.4 ⅛″ SCH 80 8.7 9.6 10.5 11.3 12.2 13.1 13.9¼″ SCH 80 17.2 18.9 20.6 22.3 24.1 25.8 27.5 ⅜″ SCH 80 33.7 37.1 40.543.8 47.2 50.6 53.9 ½″ SCH 80 56.2 61.8 67.4 73.0 78.6 84.2 89.9 ¾″ SCH80 103.7 114.1 124.5 134.8 145.2 155.6 166.0 1″ SCH 80 172.5 189.8 207.1224.3 241.6 258.8 276.1 1 ¼″ SCH 80 307.7 338.5 369.3 400.0 430.8 461.6492.3 1 ½″ SCH 80 423.9 466.3 508.7 551.1 593.5 635.9 678.2 ½″ SCH 16040.6 44.6 48.7 52.7 56.8 60.8 64.9 ¾″ SCH 160 70.6 77.6 84.7 91.7 98.8105.8 112.9 1″ SCH 160 125.1 137.7 150.2 162.7 175.2 187.7 200.2 1 ¼″SCH 160 253.5 278.9 304.2 329.6 354.9 380.3 405.6 1 ½″ SCH 160 337.3371.0 404.7 438.5 472.2 505.9 539.7

TABLE 19 Drive Delta-P = (psi) 2250 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 3.1 4.66.1 7.7 9.2 10.7 12.3 13.8 ¼″ SCH 40 5.6 8.4 11.2 14.0 16.8 19.7 22.525.3 ⅜″ SCH 40 10.3 15.5 20.6 25.8 30.9 36.1 41.2 46.4 ½″ SCH 40 16.424.6 32.8 41.0 49.2 57.4 65.6 73.8 ¾″ SCH 40 28.8 43.2 57.6 72.0 86.3100.7 115.1 129.5 1″ SCH 40 46.6 70.0 93.3 116.6 139.9 163.3 186.6 209.91 ¼″ SCH 40 80.7 121.1 161.5 201.8 242.2 282.5 322.9 363.3 1 ½″ SCH 40109.9 164.8 219.8 274.7 329.6 384.6 439.5 494.5 ⅛″ SCH 80 2.0 2.9 3.94.9 5.9 6.9 7.8 8.8 ¼″ SCH 80 3.9 5.8 7.7 9.7 11.6 13.5 15.5 17.4 ⅜″ SCH80 7.6 11.4 15.2 19.0 22.8 26.5 30.3 34.1 ½″ SCH 80 12.6 19.0 25.3 31.637.9 44.2 50.5 56.9 ¾″ SCH 80 23.3 35.0 46.7 58.3 70.0 81.7 93.4 105.01″ SCH 80 38.8 58.2 77.6 97.1 116.5 135.9 155.3 174.7 1 ¼″ SCH 80 69.2103.9 138.5 173.1 207.7 242.3 276.9 311.6 1 ½″ SCH 80 95.4 143.1 190.8238.4 286.1 333.8 381.5 429.2 ½″ SCH 160 9.1 13.7 18.3 22.8 27.4 31.936.5 41.1 ¾″ SCH 160 15.9 23.8 31.8 39.7 47.6 55.6 63.5 71.4 1″ SCH 16028.2 42.2 56.3 70.4 84.5 98.5 112.6 126.7 1 ¼″ SCH 160 57.0 85.6 114.1142.6 171.1 199.6 228.2 256.7 1 ½″ SCH 160 75.9 113.8 151.8 189.7 227.7265.6 303.6 341.5 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE VOLUMEVOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @ LOSS @LOSS @ LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′ 3750′4000′ SCHEDULE (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH40 15.3 16.9 18.4 19.9 21.5 23.0 24.5 ¼″ SCH 40 28.1 30.9 33.7 36.5 39.342.1 44.9 ⅜″ SCH 40 51.5 56.7 61.8 67.0 72.1 77.3 82.4 ½″ SCH 40 82.090.2 98.4 106.6 114.8 123.0 131.2 ¾″ SCH 40 143.9 158.3 172.7 187.1201.5 215.9 230.3 1″ SCH 40 233.2 256.6 279.9 303.2 326.5 349.8 373.2 1¼″ SCH 40 403.6 444.0 484.4 524.7 565.1 605.5 645.8 1 ½″ SCH 40 549.4604.3 659.3 714.2 769.2 824.1 879.0 ⅛″ SCH 80 9.8 10.8 11.8 12.7 13.714.7 15.7 ¼″ SCH 80 19.3 21.3 23.2 25.1 27.1 29.0 30.9 ⅜″ SCH 80 37.941.7 45.5 49.3 53.1 56.9 60.7 ½″ SCH 80 63.2 69.5 75.8 82.1 88.5 94.8101.1 ¾″ SCH 80 116.7 128.4 140.0 151.7 163.4 175.0 186.7 1″ SCH 80194.1 213.5 232.9 252.3 271.8 291.2 310.6 1 ¼″ SCH 80 346.2 380.8 415.4450.0 484.6 519.3 553.9 1 ½″ SCH 80 476.9 524.6 572.3 620.0 667.6 715.3763.0 ½″ SCH 160 45.6 50.2 54.8 59.3 63.9 68.4 73.0 ¾″ SCH 160 79.4 87.395.3 103.2 111.1 119.1 127.0 1″ SCH 160 140.8 154.9 168.9 183.0 197.1211.2 225.3 1 ¼″ SCH 160 285.2 313.7 342.2 370.8 399.3 427.8 456.3 1 ½″SCH 160 379.4 417.4 455.3 493.3 531.2 569.2 607.1

TABLE 20 Drive Delta-P = (psi) 2500 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEDRIVE DRIVE VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS@ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 500′ 750′1000′ 1250′ 1500′ 1750′ 2000′ 2250′ SCHEDULE (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) ⅛″ SCH 40 3.4 5.16.8 8.5 10.2 11.9 13.6 15.3 ¼″ SCH 40 6.2 9.4 12.5 15.6 18.7 21.8 25.028.1 ⅜″ SCH 40 11.4 17.2 22.9 28.6 34.3 40.1 45.8 51.5 ½″ SCH 40 18.227.3 36.4 45.6 54.7 63.8 72.9 82.0 ¾″ SCH 40 32.0 48.0 64.0 79.9 95.9111.9 127.9 143.9 1″ SCH 40 51.8 77.7 103.7 129.6 155.5 181.4 207.3233.2 1 ¼″ SCH 40 89.7 134.5 179.4 224.2 269.1 313.9 358.8 403.6 1 ½″SCH 40 122.1 183.1 244.2 305.2 366.3 427.3 488.4 549.4 ⅛″ SCH 80 2.2 3.34.4 5.4 6.5 7.6 8.7 9.8 ¼″ SCH 80 4.3 6.4 8.6 10.7 12.9 15.0 17.2 19.3⅜″ SCH 80 8.4 12.6 16.9 21.1 25.3 29.5 33.7 37.9 ½″ SCH 80 14.0 21.128.1 35.1 42.1 49.1 56.2 63.2 ¾″ SCH 80 25.9 38.9 51.9 64.8 77.8 90.8103.7 116.7 1″ SCH 80 43.1 64.7 86.3 107.8 129.4 151.0 172.5 194.1 1 ¼″SCH 80 76.9 115.4 153.9 192.3 230.8 269.2 307.7 346.2 1 ½″ SCH 80 106.0159.0 212.0 264.9 317.9 370.9 423.9 476.9 ½″ SCH 160 10.1 15.2 20.3 25.430.4 35.5 40.6 45.6 ¾″ SCH 160 17.6 26.5 35.3 44.1 52.9 61.7 70.6 79.41″ SCH 160 31.3 46.9 62.6 78.2 93.9 109.5 125.1 140.8 1 ¼″ SCH 160 63.495.1 126.8 158.4 190.1 221.8 253.5 285.2 1 ½″ SCH 160 84.3 126.5 168.6210.8 253.0 295.1 337.3 379.4 DRIVE DRIVE DRIVE DRIVE DRIVE DRIVE DRIVEVOLUME VOLUME VOLUME VOLUME VOLUME VOLUME VOLUME LOSS @ LOSS @ LOSS @LOSS @ LOSS @ LOSS @ LOSS @ PIPE SIZE/ 2500′ 2750′ 3000′ 3250′ 3500′3750′ 4000′ SCHEDULE (in{circumflex over ( )}3) (in{circumflex over( )}3) (in{circumflex over ( )}3) (in{circumflex over ( )}3)(in{circumflex over ( )}3) (in{circumflex over ( )}3) (in{circumflexover ( )}3) ⅛″ SCH 40 17.0 18.7 20.4 22.2 23.9 25.6 27.3 ¼″ SCH 40 31.234.3 37.4 40.6 43.7 46.8 49.9 ⅜″ SCH 40 57.2 63.0 68.7 74.4 80.1 85.991.6 ½″ SCH 40 91.1 100.2 109.3 118.4 127.6 136.7 145.8 ¾″ SCH 40 159.9175.9 191.9 207.9 223.9 239.8 255.8 1″ SCH 40 259.1 285.1 311.0 336.9362.8 388.7 414.6 1 ¼″ SCH 40 448.5 493.3 538.2 583.0 627.9 672.7 717.61 ½″ SCH 40 610.4 671.5 732.5 793.6 854.6 915.7 976.7 ⅛″ SCH 80 10.912.0 13.1 14.2 15.2 16.3 17.4 ¼″ SCH 80 21.5 23.6 25.8 27.9 30.1 32.234.4 ⅜″ SCH 80 42.1 46.4 50.6 54.8 59.0 63.2 67.4 ½″ SCH 80 70.2 77.284.2 91.3 98.3 105.3 112.3 ¾″ SCH 80 129.7 142.6 155.6 168.6 181.5 194.5207.5 1″ SCH 80 215.7 237.3 258.8 280.4 302.0 323.5 345.1 1 ¼″ SCH 80384.6 423.1 461.6 500.0 538.5 577.0 615.4 1 ½″ SCH 80 529.9 582.9 635.9688.8 741.8 794.8 847.8 ½″ SCH 160 50.7 55.8 60.8 65.9 71.0 76.1 81.1 ¾″SCH 160 88.2 97.0 105.8 114.7 123.5 132.3 141.1 1″ SCH 160 156.4 172.1187.7 203.4 219.0 234.6 250.3 1 ¼″ SCH 160 316.9 348.6 380.3 412.0 443.6475.3 507.0 1 ½″ SCH 160 421.6 463.8 505.9 548.1 590.2 632.4 674.6

The greater length of the conduit 546 for a given flow through conduit546, the greater the amount of energy loss due to friction of the fluidin the conduit 546. The larger the conduit 546 for a given flow throughthe conduit 546, the lesser the amount of energy loss due to friction ofthe fluid in the conduit 546. The data in Table 21 provided belowillustrate these concepts. These losses must be considered and balancedwith the compression losses discussed previously to determine an optimumdrive system configuration for the pumping system.

TABLE 21 DATA for oil Specific gravity = 0.9 Viscosity (SUS) = 220 BulkModulus (psi) = 250000 PRESSURE PRESSURE PRESSURE DROP/ DROP/ DROP/ 100FEET 100 FEET 100 FEET OF PIPE OF PIPE OF PIPE FLOW = FLOW = FLOW = PIPE10 GAL/MIN 15 GAL/MIN 20 GAL/MIN SIZE/SCHEDULE (PSI) (PSI) (PSI) ⅜″ SCH40 185.0 ½″ SCH 40 73.0 109.0 146.0 ¾″ SCH 40 24.0 36.0 47.0 1″ SCH 409.0 14.0 18.0 1¼″ SCH 40 3.0 4.5 6.0 1½″ SCH 40 2.4 3.2

The pumping apparatus of preferred embodiments is also useful inapplications where the fluid being pumped contains significantimpurities, which can cause damage to conventional pumps, such as acentrifugal pump. For example, sand grains and particles can causesubstantial and catastrophic failure to centrifugal pumps. In contrast,similarly sized particles do not cause substantial damage to the pumpsof preferred embodiments. Provided the valves are appropriately chosen,even product fluid which contains suspended rocks and other solidmaterials can be pumped using the pumps of preferred embodiments.Accordingly, the maintenance costs and costs associated with pumpfailure are greatly reduced. In addition, such a design enablesfiltration to occur after the product fluid is removed from its source,rather than requiring the pump inlet contain a filter.

Nevertheless, in some embodiments, the pumping apparatus can be fittedwith a filter or screen to reduce the risk of plugging within the pumpas illustrated in FIGS. 6A-C. The embodiment illustrated in FIGS. 6A-Calso employs a pump 600 that can be flushed or cleaned. The pump 600 issimilar to the embodiments described above in connection with FIGS. 3-5,and therefore only the differences are discussed in detail.

The pump 600 can comprise a pump inlet filter 605. In the embodimentillustrated in FIGS. 6A-C, the filter 605 is a fluid inlet screen placedin the pump housing 602. Alternatively, the filter or screen can be setoff from the exterior surface of the pump housing such that any build upon the filter does not block the pump inlet. However, in somecircumstances where the accumulation of particles is less of a concern,the filter can be placed adjacent to or within the pump inlet, asillustrated. The filtering of fluid to the inlet of a pump is well-knownin the art, and any suitable filtering or screening mechanism can beutilized. In preferred embodiments, screens that prevent sand particlesfrom entering the pump and also prevent screen clogging are utilized.For example, in some embodiments, well screens with a v-shaped opening,such as Johnson Vee-Wire® screens, can be utilized. Preferred screenshave an opening (sometimes referred to as the “slot size”) of betweenabout 0.01 inches to about 0.25 inches. These screens prevent themajority of fine sand particles from entering the pump. The openings inthe screen are preferably smaller than the smallest channel within thepump. Therefore, any particles that pass through the screen do not plugthe pump.

The size of particles permitted to flow through the pump is determinedby the size of the perforations or holes in the filter or screen.Preferably, the diameters of the perforations/holes in the filter are atleast as small as the smallest channel through which the product fluidpasses. Typically, the smallest channel is one of (a) the pump inletholes, (b) the transfer piston channel, or (c) the diameter of theopening created when either the inlet valve or the transfer piston valveopens. Therefore, any particle small enough to pass through theperforations/holes in the external filter is expected to pass throughthe pump apparatus without difficulty.

In some embodiments, one way valves are used to prevent the flow offluid from the reverse direction, e.g., from the product chamber 630 tothe transfer chamber 610, and from the transfer chamber 610 through thepump inlet 604. However allowing flow in the reverse direction isdesirable in many circumstances, such as when the pump or inlet screenhas become plugged or is no longer operating optimally. For example,sensors may detect an increased pressure drop across the inlet screen,or across one of the valves in the pump. Alternatively, the pump can beflushed at regular intervals to prevent the accumulation of particles,such as after it has been in operation for a predetermined period orafter it has pumped a predetermined amount of fluid. Accordingly, FIGS.6A-C illustrate an embodiment of a pump wherein the pump 600 is capableof allowing the reverse flow of product fluid.

In some embodiments, the pump 600 is provided with a mechanism by whichthe one-way valves, 608 (inlet valve) and 626 (transfer piston valve),are prevented from closing. In one embodiment, the one-way valves areprevented from closing only upon an increase in the power fluid pressurebeyond the normal operating pressures. In such an embodiment, theincreased pressure lifts the transfer piston 620 higher than it istypically lifted during normal operating conditions. Any mechanism whichutilizes the increased lift to prevent the valves from closing can beutilized.

In the embodiments illustrated in FIGS. 6A-C, the rod portion 624 of thetransfer piston 620 contains an inlet valve stop 627. During regularoperation of the pump 600, as illustrated in FIG. 6A and FIG. 6B, thisinlet valve stop 627 does not alter the operation of the pump 600. Whenit is necessary to prop open the inlet valve 608 and allow reverse flow,such as for flushing, cleaning, or adding chemicals for cleaning orrehabilitating a hydraulic structure, the power fluid pressure isincreased beyond the pressure utilized for normal operation of the pump,thereby lifting the transfer piston 620 higher than usual. When raisedto this higher level, the inlet valve stop 627 catches the conical checkvalve member 608, thereby preventing it from closing, as illustrated inFIG. 6C. Thus, fluid is permitted to flow from the transfer chamber 610through the pump inlet 604. The stop 627 need not be coupled to thetransfer piston 620.

A transfer piston valve stop 629 can be coupled to the upper surface ofthe transfer piston 620. As shown in FIG. 6A and FIG. 6B, the valve stop629 does not influence the operation of the pump 600 during normaloperating conditions. However, when the power fluid pressure isincreased beyond its normal operating parameters and the transfer pistonrises higher than usual, the transfer piston valve stop 629 is activatedand it prevents the transfer piston valve 626 from closing. In theembodiment illustrated, the transfer piston valve stop 629 comprises av-shaped member, a portion of which is positioned under the transferpiston valve member 626. During normal operation, this v-shaped memberdoes not prevent the transfer piston valve member 626 from lowering andsealing the transfer piston channel 625, as shown in FIG. 6A (powerstroke) and FIG. 6B (recovery stroke). However, when the piston 620rises to a predetermined level, an activator 680 applies force to thev-shaped member, thereby forcing the transfer piston valve 626 open, asillustrated in FIG. 6C. The activator 680 can take the form of a springas illustrated, a rod extending down from the top cap 660, or it can bea stop mounted on the inside of the pump housing 602 in the productchamber 630. Numerous other mechanisms for activating the piston valvestop 629 as known in the art are also suitable for use. In oneembodiment, the activator 680 is a spring, as this prevents damage tothe pump components (such as the top cap and piston) if the pressure ofthe power fluid is accidentally increased during normal operation.

Referring to FIG. 6C, if the pump becomes plugged or it is desirable toclean the pump or work on the well, the pump operator can supply powerfluid at an increased pressure. The increased pressure in the powerfluid chamber 650 lifts the transfer piston 620 beyond its highest pointduring normal operation. If the power fluid is supplied at 1000 psiduring normal operation to lift the transfer piston, the power fluidmight be supplied at 1200 psi for the stop to contact the activator. Theinlet valve stop 627 prevents the inlet valve 608 from closing.Similarly, the transfer piston valve stop 629 prevents the transferpiston valve 626 from closing. The product fluid is then permitted toflow from the pump outlet 606 into the product chamber 630, from theproduct chamber 630 to the transfer chamber 610, and from the transferchamber 610 through the pump inlet 604 to the fluid source. This allowsthe pump operators to work on the pump and the well without having toremove the pump from a borehole such as a water, oil, gas or coal bedmethane dewatering well.

In some embodiments described herein, the valves are self-actuatingone-way valves. However, the valves can optionally be electronicallycontrolled. Using standard computer process control techniques, such asthose known in the art, the opening and closing of each valve can beautomated. In such embodiments, two-way valves can be utilized. Two-wayvalves allow the pump operators to open the valves and permit flow inthe reverse direction when necessary, such as to flush an inlet orchannel that has become plugged or to clean the pump, without employingthe valve stops 627, 629 previously discussed. Accordingly, a pump withelectronically controlled valves can be flushed or cleaned withoutincreasing the power fluid pressure as described in connection with theembodiments illustrated in FIGS. 6A-C.

FIG. 7A and FIG. 7B illustrate a coaxial disconnect (HCDC) configured toallow removal of any coaxial hydraulic equipment from a coaxial pipe ortube connection without losing either of the two prime fluids. In pumpsand downhole well applications, the HCDC is connected between thecoaxial tubing installed down the well casing and the coaxial pumplocated at the bottom of the well. To replace the pump, the coaxialtubing is rolled up onto a waiting tube reel, and the pump isdisconnected from the HCDC. The HCDC allows the pump to be removedwithout losing the two fluids located within the coaxial tubing.

Referring now to FIG. 7A, the illustrated embodiment of an HCDC 701includes a top cap 702, which provides connection interfaces to both apower fluid port 703 and a product fluid port 704 of the coaxial tube. Avalve stem 707 is configured to control both the power and product fluidflows through the HCDC. A power fluid seat 711 is configured to controlflow of the power fluid. A product fluid seat 714 is configured tocontrol flow of the product fluid. A pump top cap 716 is configured tocontrol the position of the valve stem 707.

FIG. 7A illustrates the HCDC 701 in a closed position. When connected tothe coaxial tube, a power fluid chamber 705 maintains a fluid connectionwith the inner coaxial tube and a product fluid chamber 706 maintains afluid connection with the outer coaxial tube. The HCDC valve stem 707isolates the power fluid chamber 705 from a power fluid outlet 708 whena power fluid seal 710 is seated within the power fluid seat 711. Thisprevents the power fluid from flowing from the power fluid chamber 705to the power fluid outlet 708 through a power fluid valve port 709.

The HCDC valve stem 707 isolates the product fluid chamber 706 from aproduct fluid outlet 715 when a product fluid seal 713 is seated againstthe product fluid seat 714. This prevents the product fluid from flowingfrom the product fluid chamber 706 to the power fluid outlet 715 past aproduct fluid valve stem 712. An HCDC return spring 719 maintains aclosing force on the valve stem 707 to isolate both the power andproduct fluid flows.

Figure FIG. 7B illustrates the HCDC 701 in an open position. Whenconnected to the coaxial tube, the power fluid chamber 705 maintains afluid connection with the inner coaxial tube and the product fluidchamber 706 maintains a fluid connection with the outer coaxial tube.When the pump top cap 716 is connected into the bottom of the HCDC 701,the valve stem 707 is pushed up into the HCDC by the pump top cap valvestem pocket 718. The valve stem 707 is sealed to the top cap by a topcap power fluid seal 717. The HCDC power fluid outlet 708 now maintainsa fluid connection with the pump top cap power fluid chamber 720. TheHCDC product fluid outlet 715 now maintains a fluid connection with apump top cap product fluid chamber 721.

As the pump top cap 716 is inserted farther into the HCDC, a top capproduct fluid seal 722 forms a seal with the inside of the HCDC powerfluid outlet 715. As the pump top cap 716 is inserted farther into theHCDC, the valve stem 707 is pushed upwards against the return spring 719and lifts the product fluid seal 713 away from the product fluid seat714. This allows product fluid to flow between the product fluid chamber706 and the product fluid outlet 715.

As the pump top cap 716 is inserted further into the HCDC, the valvestem 707 is pushed upwards against the return spring 719 and lifts thepower fluid seal 710 out of the power fluid seat 711. This causes thetop of the valve stem 707 to enter the power fluid chamber and allowpower fluid to flow through the power fluid valve port 709 into thepower fluid outlet 708. This allows power fluid to flow between thepower fluid chamber 705 and the power fluid outlet 708.

FIG. 8A and FIG. 8B illustrate a subterranean switch pump. In general, ahydraulic subterranean switch (HSS) is configured to reduce the effectsof hydraulic fluid compression acting on the pumps of the presentdisclosure (such as those described above) at well depths. In downholewell applications, the HSS is connected between coaxial tubing, which isinstalled down the well casing, and the coaxial pump, located at thebottom of the well.

In one illustrated form of the system as discussed below, the HSS isconnected to a coaxial downhole tubing set which includes an outerproduct water tube within which are located two hydraulic power tubes.One of these tubes is pressurized to the required hydraulic pressurenecessary to drive a piston on its power stroke (as described above).The other hydraulic tube is pressurized to the required hydraulicpressure necessary to drive the piston on its recovery stroke (asdescribed above).

FIG. 8A illustrates one embodiment of an HSS 803. The HSS 803 includes apower hydraulic line 802, which provides fluid pressure required todrive the piston on its power stroke. A recovery hydraulic line 801provides fluid pressure required to drive the piston on its recoverystroke. A diverter valve stem 804 is configured to control a fluidconnection of the pump power fluid column 344 to either the power orrecovery pressure fluid flows through the HSS 803. In some embodiments aHSS valve stem cam 805 is actuated by a pump piston follower 806 toswitch between either power or recovery strokes.

Near the end of the power stroke, a pump piston follower 806 is raisedby a pump piston 320, which causes a recovery stroke cam lobe 807 toraise an HSS valve stem cam 805. This causes the valve stem 804 toswitch the position of a valve stem inlet 809 to complete the hydraulicconnection of a pump power fluid column 344 from the power hydraulicline 802 to the recovery hydraulic line 801 via the HSS valve stemoutlet 810. This initiates the recovery stroke of the pump.

Figure FIG. 8B illustrates the pump recovery stroke. Near the end of thepump recovery stroke, the pump piston follower 806 is lowered by thepump piston 320, which causes the power stroke cam lobe 808 to lower theHSS valve stem cam 805. This causes the valve stem 804 to switch theposition of the valve stem inlet 809 to complete the hydraulicconnection of the pump power fluid column 344 from the recoveryhydraulic line 801 to the power hydraulic line 802 via the HSS valvestem outlet 810. This initiates the power stroke of the pump.

FIG. 9 illustrates one embodiment of a downhole pump 900. FIG. 9A showsa cross section of an embodiment of a 3.5″ version of the pump 900. FIG.9B illustrates a detail of the connection locations for both the powerfluid 902 and product fluid 904 coaxial tubes. FIG. 9C illustrates adetail of the transfer piston 906 and the transfer valve 908 within thepiston tube and pump casing 912. FIG. 9C also illustrates the mainpiston seal 914 which separates the product fluid chamber 916 and thepower fluid chamber 918. FIG. 9D illustrates the main block 920, whichlocates the main seal 921 between the power fluid chamber 918 and thetransfer chamber 922. FIG. 9E illustrates the arrangement of the intakevalve 924 located within the bottom cap 926 of the pump assembly.

FIG. 10 illustrates another embodiment of a downhole pump 930. Thedownhole pump 930 has a configuration different than that of theembodiment of FIG. 9. The location of the power fluid and the productfluid (and related chambers for such power fluid and product fluid) areswitched from outside to inside and from inside to outside for thecoaxial pumps illustrated in FIG. 9 and FIG. 10. FIG. 10A shows a crosssection of an embodiment of a 1.5″ stacked version of the pump 930similar to the embodiment illustrated in FIG. 3. FIG. 10B illustrates adetail of the connection and static seal locations for both the powerfluid (internal) 932 and product fluid (external) 934 coaxial tubes.FIG. 10C illustrates a detail of the upper portion of the transferpiston 936 and the transfer valve 938 within the pump casing 940. FIG.10C also illustrates the main piston seal 942, which separates theproduct fluid chamber 944 and the transfer fluid chamber 946. FIG. 10Dillustrates the bottom cap 948, which locates the power fluid tube 932within the pump. FIG. 10D also illustrates the bottom piston seal 952,which separates the power fluid chamber 954 from the transfer fluidchamber 946.

FIG. 11 illustrates an embodiment of a downhole pump. The illustratedpump comprises an outer cylinder 1002 and a main cylinder 1004, whichsurrounds a piston rod 1006. A lower cylinder 1008 is present below themain cylinder 1004. A discharge stub 1010 is present extending from theouter cylinder 1002. A piston 1012 is present within the main cylinder1004. An outer top cap 1014 is attached to the outer cylinder 1002 andsurrounding the discharge stub 1010. An inner top cap 1016 is locatedbelow the outer top cap 1014 and entirely within the outer cylinder1002.

A piston check valve guide bar 1018A and a lower check valve guide bar1018B are attached to check valve guides 1020A and 1020B and check valvepins 1022A and 1022B respectively. The check valve pins 1022A and 1022Battach to check valves 1024A and 1024B respectively. When in an openposition, check valve 1024A allows liquid to flow around it. When in aclosed position, check valve 1024B prevents liquid flow.

In some embodiments the downhole pump includes a main block 1026surrounding the lower portion of the piston rod 1006. The downhole pumpalso includes a lower plate 1028, which contacts the check valve 1024Bwhen it is in a closed position and no fluid may pass therethrough. Thedownhole pump includes a piston check valve screw 1030 a lower platecheck valve screw 1032, a lower plate check valve nut 1034 asillustrated in FIG. 11. In addition, the downhole pump can include apiston reciprocating o-ring 1036 as part of the piston 1012, a main sealring 1038 as part of the main block 1026, a check valve o-ring 1040 aspart of the check valves 1024A and 1024B, a piston rod o-ring 1042 aspart of the piston rod 1006, a main block upper o-ring 1044 as part ofthe main block 1026, a main block lower o-ring 1046 as part of a lowerportion of the main block 1026, an inner top seal o-ring 1048 as part ofthe inner top cap 1016, an outer top seal o-ring 1050 as part of theouter top cap 1014 and a bottom seal o-ring 1052 as part of the lowerplate 1028.

FIG. 12 illustrates energy conversion for a conventional pump system anda pump system of the present disclosure. Both systems utilize thepotential energy of a fluid 1102 at an elevation 1100 greater thanground level 1106. The fluid 1102 flows through pipes 1104A and 1104B.In the illustrated electrically-driven pump system, the fluid in pipe1104B flows through a typical conventional system comprising a waterturbine 1108 which drives an electrical generator 1110. The generatedelectricity is routed through a typical electrical transmission systemto an electrically-driven fluid pump 1112 to extract fluid 1116 from adeep well through a pipe 1114. Due to energy conversion and transmissionlosses throughout this system, the conventional pump system with a highhead thus achieves an efficiency of not greater than about 60%. In theillustrated direct fluid-driven pump system, the fluid 1102 flows from apipe 1104A to the pump of the present disclosure 1118 used to extractwater 1116 from a deep well. This process uses a high-head water sourceand a pump of the present disclosure to achieve a measured efficiency ofup to about 96%. The high-head direct fluid-driven pump system increasesefficiency by reducing the conversion and transmission losses inherentin the electrically-driven pump system.

FIG. 13 is a graph illustrating dynamic performance of a piston pump,such as the piston pump described in U.S. Pat. No. 6,193,476 to Sweeney,which is hereby incorporated by reference in its entirety. The analysishas various applications including the need to accelerate the powercolumn fluid and the standing column fluid.

The piston pump includes a transfer piston sliding in the bore of apipe. The transfer piston, and a standing column of water, are raised bypressurizing an annular space (A₁−A₂) using either a source of water ata higher elevation (pressurehead concept) or a power piston in a powercylinder (power cylinder concept). Some embodiments are hybrid types ofpumps.

To reset the transfer piston at the end of the power stroke the pressurein the annular space must be reduced by:

-   -   releasing the water in the pressurehead concept or    -   reversing the power cylinder.

During the power stroke, the pressure created by the power column (P₂)must be greater than the pressure at the bottom of the standing column(P₁); the area that the standing column acts on (A₁) is larger than thearea that the power column acts on (A₁−A₂). This means that for thepressurehead concept the height of the power column (H₂) must be greaterthan the height of the standing column (H₁). For both the pressureheadconcept and the power cylinder concept, as the power column pressuredecreases, the annular space must increase relative to A₁. As theannular space increases the transfer area (A₂) decreases, decreasing thewater lifted per stroke.

During the recovery stroke the pressure in the annular space (P₅) mustbe less than P₁: in a pressurehead concept pump the point of release forthe power water (H₅) must be below the top of the standing column; inthe power cylinder concept pump the negative pressure created in thepower cylinder is limited to −14.7 psig, this becomes very significantif the power cylinder is located at or above the top of the standingcolumn. The standing column follows the transfer piston down thestanding column pipe during the recovery stroke and must be lifted againbefore any water can be discharged. The distance that the standingcolumn retreats is less than the stroke of the transfer piston becausesome water comes up through the transfer piston during the recoverystroke. If the transfer area (A₂) is large compared to A₁, the standingcolumn retreats only a short distance.

For the following discussion, term definitions are provided: RotR isRun-of-the-River Hydro, a pump used to boost water into a reservoir tosupport a small hydro power development; H₁ is height of the standingcolumn; P₁ is pressure at the bottom of the standing column; H₂ isheight of the primary power column; P₂ is pressure created by theprimary power column; P₃ is pressure in the intake chamber; P₄ ispressure during power stroke; P₁ is pressure during the recovery stroke;P₄ is pressure in the pool of working fluid; H₅ is height of the powercolumn discharge; P₅ is pressure created by the power column whiledischarging; P_(c) is pressure in the power cylinder; A₁ is area of thetransfer piston; A₂ is area of the transfer space of the transferpiston; A₂−A₁ is area of the annular space that the power fluid pressureacts on; A₂/A₁ is ratio of the transfer space area to the total transferpiston area (A₂/A₁=r<1); r is A₂/A₁<1; a is acceleration as a multipleof ‘g’; g is acceleration of gravity=32.2 ft/sec²; d is density of theworking fluid: 0.036 lbs/in³ for water; F_(d) is force down or resistingupward motion; F_(u) is force up or resisting downward motion; F_(n) isnet force in the direction of intended travel; R is total sealresistance to motion; W is weight of the Transfer Piston; M is mass; Sis stroke length; Eff is efficiency (work out/work in expressed as apercentage); W_(o) is work output; and W_(i) is work input.

Power water from a source at an elevation H₂ well above the top of thestanding column H₁ is used to pressurize the annular space and raise thetransfer piston and the standing column of water. The power water mustbe released at an elevation H₅ below H₁.

The force attempting to move the transfer piston up is:

F _(u) =P ₂(A ₁ −A ₂)+P ₃(A ₂)

For most applications P₃=P₄ and can be taken to 0 (W is much less thanthe other forces and is ignored for this analysis).

The force resisting the attempted upward motion is:

F _(d) =P ₁ A ₁ +R+W

The net force acting on the transfer piston is:

F _(n) =P ₂(A ₁ −A ₂)−(P ₁ A ₁ +R)

The mass to be accelerated is:

M=H ₁ A ₁ d+H ₂(A ₁ −A ₂)d+W

wherein the mass of the standing column is H₁A₁d; the mass of the powercolumn is H₂(A₁−A₂)d; and the mass of the piston is W (the piston massis usually small enough relative to the water columns to be ignored).Because P is HAd/A, therefore PA is HAd and P is Hd.

The masses of the water columns can be rewritten:

M=P ₁ A ₁ +P ₂(A ₁ −A ₂)

The net force is equal to the mass times the acceleration expressed as afraction of g.

F_(n) = Ma P₂(A₁ − A₂) − (P₁A₁ + R) = a{P₁A₁ + P₂(A₁ − A₂)}P₂A₁ − P₂A₂ − P₁A₁ − R = aP₁A₁ + aP₂A₁ − aP₂A₂ Separate   P₂P₂A₁ − P₂A₂ − aP₂A₁ + aP₂A₂ = aP₁A₁ + P₁A₁ + RP₂(A₁ − A₂ − aA₁ + aA₂) = P₁A₁(a + 1) + Rr = A₂/A₁, then  A₂ = rA₁, P₂(A₁ − rA₁ − aA₁ + arA₁) = P₁A₁(a + 1) + R${P_{2} = {\frac{P_{1}{A_{1}( {a + 1} )}}{( {A_{1} - {rA}_{1} - {aA}_{1} + {arA}_{1}} )} + \frac{R}{( {A_{1} - {rA}_{1} - {aA}_{1} + {arA}_{1}} )}}},{P_{2} = {\frac{P_{1}{A_{1}( {a + 1} )}}{A_{1}( {1 - r - a + {ar}} )} + \frac{R}{A_{1}( {1 - r - a + {ar}} )}}},{P_{2} = {\frac{P_{1}( {1 + a} )}{\{ {1 - r + {a( {r - 1} )}} \}} + \frac{R}{A_{1}\{ {1 - r + {a( {r - 1} )}} \}}}},{{{However}\text{:}\mspace{11mu} \{ {1 - r + {a( {r - 1} )}} \}} = {\{ {( {1 - r} ) - {a( {1 - r} )}} \} = {( {1 - a} )( {1 - r} )}}}$${P_{2} = {\frac{P_{1}( {1 + a} )}{( {1 - a} )( {1 - r} )} + \frac{R}{{A_{1}( {1 - a} )}( {1 - r} )}}},{{{Neglecting}\mspace{14mu} {R.\text{}\frac{P_{2}}{P_{1}}}} = {\frac{( {1 + a} )}{( {1 - a} )( {1 - r} )}\mspace{14mu} {or}}}$$P_{2} = \frac{P_{1}( {1 + a} )}{( {1 - a} )( {1 - r} )}$Setting  A₂/A₁ = r = 0.8:1 − r = 0.2${{\frac{P_{2}}{P_{1}} = \frac{( {1 + a} )}{( {1 - a} )0.2}},}\mspace{14mu}$

for H₁=100′, the following relationships hold:

a P₂/P₁ H₂ 0.1 6.11 611′ 0.25 8.33 833′ 0.5 15 1500′  1.0 infinite

Making the transfer area (A₂) smaller makes the annular area (A₁−A₂)bigger:

Setting  A₂/A₁ = r = 0.5:1 − r = 0.5$\frac{P_{2}}{P_{1}} = \frac{( {1 + a} )}{( {1 - a} )0.5}$

for H₁=100′, the following relationships hold:

a P₂/P₁ H₂ 0.1 2.44 244′ 0.25 3.33 333′ 0.5 6.00 600′ 1.0 infinite

The force trying to push the transfer piston down as part of a recoverystroke is:

F _(d) =P ₁ A ₁ +W

wherein W<<less than other forces and is ignored.

The force resisting the attempted downward motion is:

F _(u) =P ₅(A ₁ −A ₂)+P ₃ A ₂ +R

In this case P₃=P₁ and the valve in the transfer piston is open.

F _(n) =F _(d) −F _(u) =P ₁ A ₁−(P ₅(A ₁ −A ₂)+P ₁ A ₂ +R)

The mass to be accelerated is:

M = H₁A₁d + H₅(A₁ − A₂)d = P₁A₁ + P₅(A₁ − A₂) F_(n) = MaP₁A₁ − P₅(A₁ − A₂) − P₁A₂ − R = a{P₁A₁ + P₅(A₁ − A₂)}P₁A₁ − P₁A₂ − P₅A₁ + P₅A₂ − R = aP₁A₁ + aP₅A₁ − aP₅A₂Separate  P₅:P₅A₂ − P₅A₁ + aP₅A₂ − aP₅A₁ = aP₁A₁ − P₁A₁ + P₁A₂ + RA₂/A₁ = r:  therefore  A₂ = rA₁, P₅(rA₁ − A₁ + arA₁ − aA₁) = P₁(aA₁ − A₁ + rA₁) + R${P_{5} = {\frac{P_{1}{A_{1}( {a - 1 + r} )}}{A_{1}( {r - 1 + {ar} - a} )} + \frac{R}{A_{1}( {r - 1 + {ar} - a} )}}},{P_{5} = {\frac{P_{1}( {a - 1 + r} )}{( {r - 1 + {ar} - a} )} + \frac{R}{A_{1}( {r - 1 + {ar} - a} )}}},{{{However}\mspace{14mu} ( {r - 1 + {ar} - a} )} = {{r - 1 + {a( {r - 1} )}} = {( {1 + a} )( {r - 1} )}}}$and  a − 1 + r = a − (1 − r)${P_{5} = {\frac{P_{1}( {a - ( {1 - r} )} )}{( {1 + a} )( {r - 1} )} + \frac{R}{{A_{1}( {1 + a} )}( {r - 1} )}}},{{{Neglecting}\mspace{14mu} {R.P_{5}}} = \frac{P_{1}( {a( {1 - r} )} )}{( {1 + a} )( {r - 1} )}}$Setting  A₂/A₁ = r = 0.8:  (1 − r) = 0.2:  (r − 1) = −0.2$\frac{P_{5}}{P_{1}} = \frac{( {a - 0.2} )}{{- 0.2}( {1 + a} )}$

For H₁=100′, the following relationships hold:

a P₅/P₁ H₅ 0.1 0.455 45.5′ 0.15 0.217 21.7′ 0.2 0 0′  0.25 −0.2 −20′*  *i.e. the discharge must be below the level of the pump and create asuction

Decreasing the Transfer Area relative to the Standing Column Area:

Setting  A₂/A₁ = r = 0.5:  (1 − r) = 0.5:  (r − 1) = −0.5$\frac{P_{2}}{P_{1}} = \frac{( {a - 0.5} )}{{- 0.5}( {1 + a} )}$

For H₁=100′, the following relationships hold:

a P₅/P₁ H₅ 0.1 0.73 73′ 0.15 0.61 61′ 0.2 0.40 40′ 0.5 0.00  0′

  Work  out = weight  moved  per  stroke × H₁  W_(o) = A₂SdH₁Work  in = the  weight  of  water  used  per  stroke × total  height  lost  W_(i) = (A₁ − A₂)Sd(H₂ − H₅)$\mspace{20mu} {{{Eff} = {{100\; W_{o}\text{/}W_{i}} = \frac{A_{2}{SdH}_{1}}{( {A_{1} - A_{2}} ){{Sd}( {H_{2} - H_{5}} )}}}},{{A_{2}\text{/}A_{1}} = {{r\text{:}A_{2}} = {rA}_{1}}},\mspace{20mu} {{Eff} = \frac{100\; {rA}_{1}H_{1}}{{A_{1}( {1 - r} )}( {H_{2} - H_{5}} )}},\mspace{20mu} {{Eff} = \frac{100\; {rH}_{1}}{( {1 - r} )( {H_{2} - H_{5}} )}},}$

As an example

A₂/A₁ = r = 0.8:1 − r = 0.2:  and  a = 0.1  g:  H₁ = 100  ft, H₂ = 611^(′):  H₅ = 45.5^(′)${Eff} = {\frac{100(0.8)100}{0.2( {611 - 45.5} )} = {70.7\%}}$

In order to de-water a mine the equations discussed above can be used,but the power water can be released at H₅=0. However, the pressurerequired to operate the power stroke is not reduced and the water isreleased at the bottom of the standing column reducing the efficiency(to 65.5% in one situation above). The released power water then has tobe re-lifted resulting in a further efficiency loss (to 52.4% in onesituation investigated above).

The placement of the pump does not change the basic formulas, but doesaffect how the formulas may be simplified.

The force attempting to move the transfer piston up is F_(u):

F _(u) =P ₂(A ₁ −A ₂)+P ₃(A ₂)

-   -   P₃=P₄ is nearly 0 in most cases and is ignored.

The force resisting the attempted upward motion is F_(d) (W is much lessthan the other forces and is ignored for this analysis):

F _(d) =P ₁ A ₁ +R+W

F _(n) =F _(u) −F _(d) =P ₂(A ₁ −A ₂)−(P ₁ A ₁ +R)

Where the mass of the Standing Column H₁A₁d, the mass of the powercolumn H₂(A₁−A₂)d; and the mass of the piston W, the mass to beaccelerated is (the piston mass is usually small enough relative to thewater columns to be ignored):

H₂ = H₁:  HAd = PdMass = H₁A₁d + H₁(A₁ − A₂)d + W = 2H₁A₁d − H₁A₂d     = 2P₁A₁ − P₁A₂F_(n) = Ma P₂(A₁ − A₂) − (P₁A₁ + R) = (2P₁A₁ − P₁A₂)aP₂ = P₁ + P_(c):  and  A₂ = rA₁:(P₁ + P_(c))(A₁ − rA₁) − P₁A₁ − R = (2P₁A₁ − P₁rA₁)aP₁A₁ + P_(c)A₁ − P₁rA₁ − P_(c)rA₁ − P₁A₁ − R = aP₁A₁(2 − r)Separate  P_(c), P_(c)A₁ − P_(c)rA₁ = aP₁A₁(2 − r) + P₁rA₁ + RP_(c)A₁(1 − r) = P₁A₁(a(2 − r) + r) + R${P_{c} = {\frac{P_{1}{A_{1}( {{a( {2 - r} )} + r} )}}{A_{1}( {1 - r} )} + \frac{R}{A_{1}( {1 - r} )}}},{P_{c} = {\frac{P_{1}( {{a( {2 - r} )} + r} )}{( {1 - r} )} + \frac{R}{A_{1}( {1 - r} )}}},{{{Neglecting}\mspace{14mu} {R.\text{}P_{c}}} = {\frac{P_{1}( {{a( {2 - r} )} + r} )}{( {1 - r} )}\text{;}}}$Set  r = 0.8:  (1 − r) = 0.2:  (2 − r) = 1.2$P_{c} = \frac{P_{1}( {{1.2a} + 0.8} )}{0.2}$

Where H₁=100 ft and P₁=43.3 psig, the following relationships apply:

a P_(c)/P₁ P_(c) P₂ 0.0 4.0 0.1 4.6 199′ 242′ 0.25 5.5 0.5 7.0 1.0 10.0

Decrease the transfer area so that:

A₂/A₁ = r = 0.5;1 − r = 0.5:  2 − r = 1.5$P_{c} = \frac{P_{1}( {{1.5\; a} + 0.5} )}{0.5}$

Where H₁=100 ft and P₁=43.3 psig, the following relationships apply:

a P_(c)/P₁ P_(c) P₂ 0.0 1.0 0.1 1.3 56.3′ 100′ 0.25 1.75 0.5 2.5

The force attempting to push the transfer piston down is (W is much lessthan other forces and is ignored):

F _(d) =P ₁ A ₁ +W

The force resisting the attempted downward motion is:

F _(u) =P ₅(A ₁ −A ₂)+P ₃ A ₂ +R

-   -   In this case P₃=P₁: the transfer valve is open,

F _(n) =F _(d) −F _(u) =P ₁ A ₁−(P ₅(A ₁ −A ₂)+P ₁ A ₂ +R)

The mass to be accelerated is:

  M = H₁A₁d + H₂(A₁ − A₂)d;  H₂ = H₁:  H₁d = P₁ :   M = P₁A₁ + P₁(A₁ − A₂)  F_(n) = Ma  P₁A₁ − P₅(A₁ − A₂) − P₁A₂ − R = a(P₁A₁ + P₁(A₁ − A₂))  A₂ = rA₁:  P₅ = P₁ + P_(c)(P_(c)  is  negative)P₁A₁ − (P₁ + P_(c))(A₁ − rA₁) − P₁rA₁ − R = aP₁A₁ + aP₁A₁ − aP₁rA₁P₁A₁ − (P₁A₁ + P_(c)A₁ − P₁rA₁ − P_(c)rA₁) − rP₁A₁ = aP₁A₁(2 − r) + RP₁A₁ − P₁A₁ − P_(c)A₁ + rP₁A₁ + P_(c)rA₁ − rP₁A₁ = aP₁A₁(2 − r) + R  P_(c)rA₁ − P_(c)A₁ = aP₁A₁(2 − r) + R  P_(c)A₁(r − 1) = aP₁A₁(2 − r) + R$\mspace{20mu} {{P_{c} = {\frac{{aP}_{1}{A_{1}( {2 - r} )}}{A_{1}( {r - 1} )} + \frac{R}{A_{1}( {r - 1} )}}},\mspace{20mu} {P_{c} = {\frac{{aP}_{1}( {2 - r} )}{( {r - 1} )} + \frac{R}{A_{1}( {r - 1} )}}},\mspace{20mu} {{{Neglecting}\mspace{14mu} {R.\mspace{20mu} P_{c}}} = \frac{{aP}_{1}( {2 - r} )}{( {r - 1} )}}}$  Setting  A₂/A₁ = r = 0.8 ; (2 − r) = 1.2 ;  (r − 1) = −0.2 ; (2 − r)/(r − 1) = −6   P_(c) = −6aP₁

If H₁=100 ft and P₁=43.3 psig, the following relationships apply:

a P_(c) = −6aP₁ 0.1 −26 psig (not possible) 0.05 −13 psig (limitingcase)

To have P_(c)=−14.7, for a=0.1, P₁=(−14.7)/(−0.6)=24.5 psig: H₁=56.6 ft.

Making the transfer area smaller:

Setting A₂/A₁=r=0.5; (2−r)=1.5; (r−1)=−0.5; (2−r)/(r−1)=−3

P_(c)=−3aP₁:

For P₁=43.3 psig (100 ft of water), a is 0.1 and P_(c) is −13 psig.

Work out=weight moved per stroke×H₁

W_(o)=A₂SdH₁

Work in=W_(i)=P_(c)(A₁−A₂)S:

-   -   P_(c)=P_(c)(power)−P_(c)(recovery)

The volume moved by the power cylinder must equal the volume received bythe power side of the transfer cylinder; (A₁−A₂)S.

${Eff} = {{100\mspace{14mu} W_{o}\text{/}W_{i}} = \frac{100\mspace{14mu} A_{2}{SdH}_{1}}{{P_{c}( {A_{1} - A_{2}} )}S}}$A₂/A₁ = r:  A₂ = rA₁:  and  HAd = PA:  Hd = P${Eff} = \frac{100\; {rA}_{1}P_{1}}{P_{c}{A_{1}( {1 - r} )}}$${Eff} = \frac{100\; {rP}_{1}}{P_{c}( {1 - r} )}$A₂/A₁ = r = 0.8:  (1 − r) = 0.2:  and  H₁ = 100  ft^(′):  P₁ = 43.3  psigPower  stroke   acceleration  of  0.1  gand  accepting  a  recovery  acceleration  of  0.05  g, Power   Stroke  P_(c) = 199Recovery  Stroke  P_(c) = −13 P_(c) = 212  psig${Eff} = {\frac{100(0.8)43.3}{212(0.2)} = {81.7\%}}$

In a pump placed at the bottom of a standing column H₂=0 (RotR HydroStyle 1), (for mine dewatering and booster applications), the forceattempting to move the transfer piston up is F_(u):

F _(u) =P ₂(A ₁ −A ₂)+P ₄(A ₂)

-   -   P₄=P₃ is nearly 0 in most cases and is ignored.

The force resisting the attempted upward motion is F_(d) (wherein W ismuch smaller than the other forces and is ignored for this analysis):

F _(d) =P ₁ A ₁ R+W

F _(n) =F _(u) −F _(d) =P ₂(A ₁ −A ₂)−(P ₁ A ₁ +R)

Where the mass of the Standing Column is H₁A₁d; the mass of the powercolumn is H₂(A₁−A₂)d=0; and the mass of the piston W (the piston mass isusually small enough relative to the water columns to be ignored), themass to be accelerated is:

:  HAd = PA Mass = H₁A₁d + W = P₁A₁ F_(n) = MaP₂(A₁ − A₂) − (P₁A₁ + R) = P₁A₁a P₂ = P_(c):  A₂ = rA₁P_(c)(A₁ − rA₁) − P₁A₁ − R = P₁A₁aP_(c)A₁(1 − r) = P₁A₁a + P₁A₁ + R${P_{c} = {\frac{P_{1}{A_{1}( {a + 1} )}}{A_{1}( {1 - r} )} + \frac{R}{A_{1}( {1 - r} )}}},{P_{c} = {\frac{P_{1}( {a + 1} )}{( {1 - r} )} + \frac{R}{A_{1}( {1 - r} )}}},{{{Neglecting}\mspace{14mu} {R.P_{c}}} = \frac{P_{1}( {a + 1} )}{( {1 - r} )}}$Set  r = 0.8:  (1 − r) = 0.2

For H₁=100′ (P₁=43.3 psig), the following relationships apply:

a P_(c)/P₁ P_(c) 0.1 5.5 238 psig 0.25 6.25 271 psig

F _(d) =P ₁ A ₁ +W

(wherein W is much less than other forces and is ignored)

The force resisting the attempted downward motion is F_(u):

F _(u) =P ₅(A ₁ −A ₂)+P ₃ A ₂ +R

-   -   In this case P₃=P₁: the Transfer Valve is open.

F _(n) =F _(d) −F _(u) =P ₁ A ₁−(P ₅(A ₁ −A ₂)+P ₁ A ₂ +R)

The mass to be accelerated is:

M = H₁A₁d + H₅(A₁ − A₂)d;  H₅ = 0:  H₁d = P₁: M = P₁A₁F_(n) = Ma P₁A₁ − P₅(A₁ − A₂) − P₁A₂ − R = aP₁A₁A₂ = rA₁:  P₅ = P_(c)(P_(c)  is  negative)${{{P_{1}A_{1}} - {P_{c}( {A_{1} - {rA}_{1}} )} - {P_{1}{rA}_{1}}} = {{{{aP}_{1}A_{1}} + R - {P_{c}{A_{1}( {1 - r} )}}} = {{{{aP}_{1}A_{1}} - {P_{1}A_{1}} + {P_{1}{rA}_{1}} + {RP_{c}{A_{1}( {r - 1} )}}} = {{{{aP}_{1}A_{1}} - {P_{1}A_{1}} + {P_{1}{rA}_{1}} + {RP_{c}}} = {\frac{P_{1}{A_{1}( {a - 1 + r} )}}{A_{1}( {r - 1} )} + \frac{R}{A_{1}( {r - 1} )}}}}}},{P_{c} = {\frac{P_{1}( {a - 1 + r} )}{( {r - 1} )} + \frac{R}{A_{1}( {r - 1} )}}},{{{Neglecting}\mspace{14mu} {R.P_{c}}} = {\frac{P_{1}( {a - 1 + r} )}{( {r - 1} )} = {{\frac{P_{1}( {a + ( {r - 1} )} )}{( {r - 1} )}{Set}\mspace{14mu} A_{2}\text{/}A_{1}} = {r = {{{0.8\text{:}\mspace{11mu} r} - 1} = {{{- 0.2}P_{c}} = \frac{P_{1}( {a - 0.2} )}{- 0.2}}}}}}}$

For H₁=100′ (P1=43.3 psig), the following relationships apply:

a P_(c)/P₁ P_(c) 0.1 0.5 21.65 psig 0.2 0    0 psig 0.25 −0.25 −10.8psig

If the Recovery Stroke work can be recovered

-   -   W_(o)=A₂SdH₁    -   Work in=W_(i)=P_(c)(A₁−A₂)S:    -   P_(c)=P_(c)(power)−P_(c)(recovery)

The volume moved by the power cylinder must equal the volume received bythe annular space of the transfer cylinder; (A₁−A₂)S.

${Eff} = {{100\mspace{14mu} W_{o}\text{/}W_{i}} = \frac{100A_{2}{SdH}_{1}}{{P_{c}( {A_{1} - A_{2}} )}S}}$A₂/A₁ = r :  A₂ = rA₁:  and  HAd = PA:  Hd = P${Eff} = \frac{100\; {rA}_{1}P_{1}}{P_{c}{A_{1}( {1 - r} )}}$${Eff} = \frac{100\; {rP}_{1}}{P_{c}( {1 - r} )}$A₂/A₁ = r = 0.8:1 − r = 0.2:  and  H₁ = 100  ft^(′):  P₁ = 43.3  psigPower  and  Recovery  Stroke  acceleration  of  0.1  gPower  Stroke  P_(c) = 238 Recovery  Stroke  P_(c) = 22P_(c) = 216  psig${Eff} = {\frac{100(0.8)43.3}{216(0.2)} = {81.7\%}}$

If the recovery stroke work cannot be salvaged:

${Eff} = \frac{100\; {rP}_{1}}{P_{c}( {1 - r} )}$Power  Stroke  P_(c) = 238 Recovery  Stroke  P_(c) = 0P_(c) = 238  psig${Eff} = {\frac{100(0.8)43.3}{238(0.2)} = {72.7\%}}$

Although the above analysis works in the general case, severalprinciples put forth above can have a more nuanced analysis. Repeatingbelow a portion of the equations mentioned above:

Work  out = weight  moved  per  stroke × H₁ W_(o) = A₂SdH₁Work  in = the   weight  of  water  used  per  stroke × total  height   lostW_(i) = (A₁ − A₂)Sd(H₂ − H₅)${Eff} = {{100\mspace{14mu} W_{o}\text{/}W_{i}} = \frac{100\; A_{2}{SdH}_{1}}{( {A_{1} - A_{2}} ){{Sd}( {H_{2} - H_{5}} )}}}$Bold  terms  cancel${{A_{2}\text{/}A_{1}} = {{r\text{:}\mspace{11mu} A_{2}} = {rA}_{1}}},{{Eff} = \frac{100{rA}_{1}H_{1}}{{A_{1}( {1 - r} )}( {H_{2} - H_{5}} )}},{{Eff} = \frac{100{rH}_{1}}{( {1 - r} )( {H_{2} - H_{5}} )}},$

In the first analysis, efficiency increases with increasing “r” becausethe upper term increases with “r” and the first factor in the lower termdecreases with increasing “r”: both trends act to increase theefficiency with increasing “r”. However, the second factor in the lowerterm decreases with increasing “r”, i.e. the pump is easier to drivewith smaller “r”; and therefore H₂ (the height of the required powerfluid column) decreases and H₅ (the allowable height of the power fluidrelease) increases. Other work supported the trend of increasingefficiency with increasing “r”.

Nevertheless, certain formulae are reproduced below to clarify thegeneral case.

From Power Stroke Considerations:

${P_{2} = {\frac{P_{1}( {1 + a} )}{( {1 - a} )( {1 - r} )} + \frac{R}{{A_{1}( {1 - a} )}( {1 - r} )}}},{{{Neglecting}\mspace{14mu} {R.\text{}P_{2}}} = \frac{P_{1}( {1 + a} )}{( {1 - a} )( {1 - r} )}}$

From Recovery Stroke Considerations:

${P_{5} = {\frac{P_{1}( {a - ( {1 - r} )} )}{( {1 + a} )( {r - 1} )} + \frac{R}{{A_{1}( {1 + a} )}( {r - 1} )}}},{{{Neglecting}\mspace{14mu} {R.P_{5}}} = \frac{P_{1}( {a - ( {1 - r} )} )}{( {1 + a} )( {r - 1} )}}$

For pressurehead style pumps P₁, P₂ and P₅ can be used in place of H₁,H₂ and H₅.

The efficiency equation can be rewritten as:

${{Eff} = \frac{100\; {rA}_{1}P_{1}}{{A_{1}( {1 - r} )}( {P_{2} - P_{5}} )}},{= \frac{100\; {rP}_{1}}{{( {1 - r} )P_{2}} - {( {1 - r} )P_{5}}}},{{Eff} = \frac{100\; {rP}_{1}}{\frac{( {1 - r} )( {P_{1}( {1 + a} )} }{( {1 - a} )( {1 - r} )} - \frac{( {1 - r} ){P_{1}( {a - ( {1 - r} )} )}}{( {1 + a} )( {r - 1} )}}},{{{- ( {1 - r} )}\mspace{14mu} {can}{\mspace{11mu} \;}{be}\mspace{14mu} {rewritten}\mspace{14mu} {as}} + ( {r - 1} )}$${{{Eff} = \frac{100\; r}{\frac{( {1 - r} )( {1 + a} )}{( {1 - a} )( {1 - r} )} + \frac{( {r - 1} )( {a - ( {1 - r} )} )}{( {1 + a} )( {r - 1} )}}},{{Eff} = \frac{100\; r}{\frac{( {1 + a} )}{( {1 - a} )} + \frac{( {a - ( {1 - r} )} )}{( {1 + a} )}}},}\mspace{14mu}$

Note: as “r” increases, the top term increases. The first term in thebottom is independent of “r”: the second term on the bottom increases as“r” increases, reducing the efficiency with increasing “r”; however thebottom doesn't increase as quickly as the top so that over all theefficiency increases with increasing “r”.

The equation is solved for four examples to demonstrate that theefficiency increases with increasing “r” for accelerations of 0.1 g and0.01 g.

Example 1: for a=0.1; and r=0.8

$\begin{matrix}{{{Eff} = \frac{100\; r}{\frac{( {1 + a} )}{( {1 - a} )} + \frac{( {a - ( {1 - r} )} )}{( {1 + a} )}}},} \\{{= \frac{80}{\frac{1.1}{0.9} + \frac{( {0.1 - 0.2} )}{1.1}}},} \\{{= \frac{80}{1.22 - \frac{0.1}{1.1}}},} \\{{= \frac{80}{1.22 - 0.091}},}\end{matrix}$ Eff = 70.9%

Example 2: for a=0.1; and r=0.5

$\begin{matrix}{{Eff} = \frac{100\; r}{\frac{( {1 + a} )}{( {1 - a} )} + \frac{( {a - ( {1 - r} )} )}{( {1 + a} )}}} \\{= \frac{50}{\frac{1.1}{0.9} + \frac{( {0.1 - 0.5} )}{1.1}}} \\{= \frac{50}{1.22 - \frac{0.4}{1.1}}} \\{= \frac{50}{1.22 - 0.364}}\end{matrix}$ Eff = 58.4%

Example 3: for a=0.01; and r=0.8

$\begin{matrix}{{Eff} = \frac{100\; r}{\frac{( {1 + a} )}{( {1 - a} )} + \frac{( {a - ( {1 - r} )} )}{( {1 + a} )}}} \\{= \frac{80}{\frac{1.01}{0.99} + \frac{( {0.01 - 0.2} )}{1.01}}} \\{= \frac{80}{1.22 - \frac{0.19}{1.01}}} \\{= \frac{80}{1.22 - 0.188}}\end{matrix}$ Eff = 71.4%

Example 4: for a=0.01; and r=0.5

$\begin{matrix}{{{Eff} = \frac{100\; r}{\frac{( {1 + a} )}{( {1 - a} )} + \frac{( {a - ( {1 - r} )} )}{( {1 + a} )}}},} \\{{= \frac{50}{\frac{1.01}{0.99} + \frac{( {0.01 - 0.5} )}{1.01}}},} \\{= \frac{50}{1.22 - \frac{0.49}{1.01}}} \\{{= \frac{50}{1.22 - 0.485}},}\end{matrix}$ Eff = 68.0%

TABLE 22a Output Cycle time 11.99 sec Cycles/min 5.00 per cycle 1.78 lbsper min 8.92 lbs 4.05 liters 1.07 Gal (US) 0.89 Gal (Imp) Work Rate297.39 ft-lbs/sec 0.541 hp Eff 96.71%

To calculate efficiency for the Power Cylinder Option, wherein thecalculation includes the mass of the power column in the calculation ofthe acceleration, H is height of standard column, which is 2000 ft; P1is 864 psi; A1 is the area of standing column, which is 5.45 squareinches, A2/A1=0.505; A2 is 2.75225 square inches; A1−A2 is the area thatthe pressure differential operates on, which is 2.69775 square inches;R=k*H1*(A1)̂0.5; k=0.0054; R=Sum of Seal Resistance which is 25.21 lbs;Stroke is 1.5 ft; 1 ft of water (f)=0.432 psi; Density of water 0.036lbs/in3.

TABLE 22b Recovery Power Stroke column Net Recovery Ei1 (P_(c) = −12psig) height force Accel stroke Work Ratio of Hp/H1 Hp P5 psi lbsft/sec2 sec in lbs 1 2000 852 7 0.049 7.788 582.71 0.99 1980 843.36 300.212 3.766 582.71 0.975 1950 830.4 65 0.458 2.560 582.71 0.95 1900808.8 124 0.876 1.850 582.71 0.925 1850 787.2 182 1.306 1.516 582.71 0.91800 765.6 240 1.747 1.311 582.71 0.85 1700 722.4 357 2.664 1.061 582.710.8 1600 679.2 473 3.633 0.909 582.71 0.75 1500 636 590 4.657 0.803582.71 0.7 1400 592.8 706 5.741 0.723 582.71 0.5 1000 420 1173 10.7990.527 582.71 0.998 1996 850.272 12 0.082 6.058 582.71

Power Stroke Water Energy Gained Per Stroke=Eo=12SA2dH1

-   -   Eo=42803 in lbs    -   Recovery Work=583 in lbs    -   Hp=0.998×H1=1996 ft: Ph=862.272 psi

TABLE 22c Ratio of P2/P1 Height of Power required working Net forceAccel stroke Pc required Ei2 Work psi column P2 psi lbs ft/sec2 sec psiin lbs Eo/Ei 1 1996 864.0 −2403 zero — 1.73 84 — 1.5 1996 1296.0 −1238zero — 433.73 21062 197.76%  2 1996 1728.0  −72 zero — 865.73 42039100.42%  2.1 1996 1814.4  161 0.74 2.019 952.13 46235 91.43% 2.25 19961944.0  510 2.34 1.133 1081.73 52528 80.59% 2.5 1996 2160.0  1093 5.000.774 1297.73 63017 67.30% 2.75 1996 2376.0  1676 7.67 0.625 1513.7373506 57.77% 3 1996 2592.0  2259 10.34 0.539 1729.73 83995 50.61% 2.0391996 1761.7   19 0.09 5.936 899.42 43676 96.71%

As illustrated above in Tables 22, the A2/A1 ratio is 0.505, therecovery stroke show −12 psi as Pc, which shows a 12 psi vacuum iscreated under the transfer piston as the upper cylinder is drawn back.Further, only 582.71 lbs. of energy is needed to draw the transferpiston down in the cylinder because the area on the upper side of thetransfer piston with the force on it from the weight of the dischargecolumn easily overcomes the energy resisting the transfer piston fromthe lower area of the transfer piston in the transfer chamber.

Examining the power stroke, at 96.71% efficiency at an acceleration of0.09 ft/sec² 43,676 lbs. of force is needed to make the transfer pistonmove back up. The acceleration is 0.09/32=0.0028 g (gravity) as opposedto the 1.0 g used in some of the equations reproduced above and thatdescribed how the particular pump was to operate. Pipelines are designedat a nominal 2 ft/sec velocity with a maximum design velocity of 5ft/sec, which are standard numbers. Such numbers may be changed, but arethose often used. At 1 g (32 ft/sec²) the acceleration creates avelocity, which is too fast too quickly for optimal use.

Tables 22 above shows the efficiency of one 3.5″ pump at just over 35Barrels per day. The data indicate that the 3.5″ pump functions just aswell if it were 3.5′. The above 3.5″ pump has useful application instripper oil wells in the United States. Of the more than 400,000stripper oil wells in the United States, many average approximately 2.2Barrels per day of oil and simultaneously produce 9 Barrels of water.Thus, the average production of a stripper oil well is approximately 20Barrels per day. Smaller stripper oil wells use 10 HP or larger pumpjacks. As illustrated in the data of Table 22, a pump of the presentdisclosure can perform the same work as one of the commonly usedstripper oil well pumps for less than 1 HP.

TABLE 23 Efficiency vs A2/A1 A2/A1 = P2/P1 0.4 0.5 0.6 0.7 0.8 0.82 1.50.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.8 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.041.4% 0.0% 0.0% 0.0% 0.0% 0.0% 2.5 31.6% 45.7% 0.0% 0.0% 0.0% 0.0% 3.025.5% 37.2% 53.3% 0.0% 0.0% 0.0% 4.0 18.5% 27.1% 39.3% 59.1% 0.0% 0.0%5.0 14.5% 21.3% 31.2% 47.1% 0.0% 0.0% 7.5 9.4% 13.9% 20.5% 31.3% 53.7%61.1% 10.0 6.9% 10.3% 15.3% 23.5% 40.2% 45.8% optimum 26.6% 31.5% 36.0%40.7% 46.3% 47.5% P5/P1, req 0.39 0.31 0.185 0.05 0.05 0.05 Rec Acc 8.048.01 8.04 7.21 4.21 3.61 ft/sec2 P2/P1 opt 2.9 3.48 4.35 5.79 8.69 9.65

The data from Table 23 above are reproduced in the graph of FIG. 13. Asillustrated, the efficiency of the pump is graphed as a function of theratio of A2/A1 for several different values of P2/P1. Lines have beenadded connecting the points on the graph of each value of P2/P1 as theratio of A2/A1 changed. Generally, for each P2/P1 the efficiencyincreased as the ratio of A2/A1 increased up until a point whenefficiency fell to zero and remained there for further increases in theratio of A2/A1.

More accurately, the piston pump illustrated in Table 23 and FIG. 13 ismore efficient as the ratio of A2/A1 increases. There are two opposingtrends in operation: (1) as the transfer area A2 increase for a fixedoverall area A1, more fluid is lifted per stroke and less working fluidis used per stroke; and (2) the opposing trend is that the drivingpressure must increase as the transfer area increases for a fixedover-all area. As illustrated in the equations above, the increase inlifted fluid and the reduction in power fluid are more important thatthe increase in the driving pressure. The fluid lifted per stroke is thetransfer area times the stroke length (A2S). The power fluid used perstroke is the power fluid area times the stroke length. The power fluidarea is the annular area equal to the over-all area minus the transferarea (A1−A2), as A2 increases for a fixed A1, the power fluid areadecreases.

Referring to the drawings, and first to FIG. 14, this shows a pistontype pumping apparatus 20 according to an embodiment of the invention.The apparatus is intended to pump liquids, typically water, uprelatively great vertical distances, such as from the bottom 30 of amine to the surface as exemplified by the distance between points 22 and24. The system includes a vertically oriented first transfer cylinder 26having a top 28, adjacent point 24, and a bottom 30. There is a firstpassageway 32 for liquid adjacent the top where liquid is dischargedfrom the cylinder. There is a second passageway 34 near the bottom ofthe cylinder which allows liquid to enter or exit the cylinder.

A transfer piston 40 is reciprocatingly mounted within the cylinder andis connected to a vertically oriented, hollow piston rod 42 whichextends slidably and sealingly through aperture 44 in the bottom of thecylinder. The piston 40 has an area 29 at the top thereof against whichpressurized fluid in the cylinder acts. The passageway 32 is above oradjacent to the uppermost position of the piston and the passageway 34is below its lowermost position. It should be understood that FIG. 14 isa simplified drawing of the invention and seals and other conventionalelements which would be apparent to someone skilled in the art areomitted. These components would be similar to those disclosed in U.S.Pat. No. 6,913,476, which is incorporated herein by reference in itsentirety.

There is a first one-way valve 41 at the bottom of the piston rod 42which includes a valve member 43 and a valve seat 45 which extends abouta third passageway 47 in bottom 49 of the piston rod. This one-way valveallows liquid to flow into the piston rod, but prevents a reverse flowout the bottom of the piston rod.

There is a reload chamber 46 below the cylinder 26 which is sealed,apart from aperture 48 at top 50 thereof, which slidably and sealinglyreceives piston rod 42, and fourth passageway 52 at bottom 54 thereof.The piston rod acts as a piston within the reload chamber. There couldbe a piston member on the end of the rod within the reload chamber andthe term “piston rod” includes this possibility. A second one-way valve56 is located at the passageway 52 and includes a valve member in theform of ball 58 and a valve seat 60 adjacent to the bottom of the reloadchamber. An annular stop 62 limits upward movement of the ball. Thisone-way valve allows liquid to flow from a source chamber 70 into thereload chamber 46, but prevents liquid from flowing from the reloadchamber towards the chamber 70. Chamber 70 contains liquid to be pumpedout of passageway 32 at top of the cylinder.

The piston 40 has a diameter D1 substantially greater than diameter D2of the piston rod and, accordingly, the piston rod, acting as a pistonin the reload chamber, has a significantly smaller area upon whichpressurized liquid acts, in the direction of movement of the piston rodand piston 40, within the reload chamber 46 compared to thecross-sectional area of the piston 40 and the interior of cylinder 26.For example, in one embodiment the piston is 3″ in diameter, while thepiston rod 42 is 1″ in diameter. Therefore liquid in the cylinder at agiven pressure exerts a much greater force on the piston and piston rodcompared to the force exerted upwardly on the piston rod and piston by asimilar pressure of liquid in reload chamber 70.

There is means 80 for storing pressurized liquid 82 connected to thesecond passageway 34. This means 80 stores pressurized liquid recoveredfrom chamber 90 in the cylinder 26 below the piston 40. In thisembodiment the means includes a column of liquid 92 extending frompassageway 34 to a point 94 at the top of the column. The column in thisexample is formed by an annular jacket 96 extending about the cylinder26 and a conduit 98 extending to discharge end 100 of a second, powercylinder 102. The column can be pressurized by a remotely located powercylinder or by using a body of liquid (water), located at a higherelevation, as a pressure head.

The cylinder 102 has a piston 104 reciprocatingly mounted therein. Theliquid 82 occupies chamber 106 on side 108 of the piston which facesdischarge end 100 of the cylinder. Chamber 110 on the opposite side ofthe piston is vented to atmosphere through passageway 112. There is apiston rod 114 connected to the piston 104 to drive the piston towardsthe discharge end and thereby discharge liquid 82 from the cylinder.

In operation, the cylinder 26 is filled with liquid, typically water,above the piston 40. Likewise chamber 90 is filled with water along withthe jacket 96 and chamber 106 of the second cylinder 102. Similarlypiston rod 42 is filled with water or other liquid along with the reloadchamber 46 and the source chamber 70. The piston is in the lowermostposition as shown in FIG. 14. This is used to prime the pump.

The piston rod 114 is then moved to the left, from the point of view ofFIG. 14, typically by a motor or engine with a crank mechanism or apneumatic or hydraulic device, although this could be done in otherways. This displaces liquid 82 from the cylinder 102 downwardly throughthe column 92, through the second passageway 34 into the chamber 90where it acts upwardly against the bottom of piston 40 and pushes thepiston upwards in the cylinder 26.

The piston rod 42 is pushed upwardly with the piston and thereby reducespressure in reload chamber 46, since the volume occupied by the pistonrod in the reload chamber is reduced as the piston rod moves upwardly.One-way valve 41 prevents liquid from flowing from the piston rod intothe reload chamber, but the reduced pressure within the reload chambercauses ball 58 to raise off of its seat 60, such that liquid flows fromchamber 70 into the reload chamber.

When piston 104 of the cylinder 102 approaches the end of its traveladjacent discharge end 100, and piston 40 approaches its uppermostposition towards top 28 of the cylinder 26, liquid is discharged fromthe passageway 32. When the piston 104 has reached its limit adjacentdischarge end 100, pressure against piston rod 114 is released. Theweight of liquid occupying cylinder 26 above the piston 40 actsdownwardly on the piston and forces the piston towards its lowermostposition shown in FIG. 14. This forces liquid out of chamber 90 and intothe chamber 106 of cylinder 102, moving the piston 104 to the right,from the point of view of FIG. 14, so it returns to the originalposition shown.

At the same time, the piston rod 42 is forced downwardly into the reloadchamber 46. This increases pressure in the reload chamber and keeps theball 58 against valve seat 60 to prevent liquid from flowing back intothe source chamber 70 through the passageway 52. The liquid in thereload chamber is thus forced upwardly into the piston rod 42 by raisingvalve member 43 off of valve seat 45. In this way, a portion of theliquid in reload chamber 46, which had flowed into the reload chamberfrom the source chamber as the piston was previously raised, moves fromthe reload chamber into the piston rod and refills the cylinder 26 abovethe piston 40 as the piston moves downwardly towards its lowermostposition shown in FIG. 14.

The piston 104 in the cylinder 102 is then pushed again to the left,from the point of view of FIG. 14, and again raises the piston 40. Avolume of liquid equal to the volume of liquid which moved into thepiston rod 42 from the reload chamber 46, as the piston 40 previouslymoved downwards, is then discharged from passageway 32 as the piston 40approaches its uppermost position and piston 102 approaches its positionclosest to the discharge end 100 of cylinder 102.

The cycles are then continued and, as may be readily understood, eachtime the piston 40 moves down and back up, it pumps a volume of liquidfrom the reload chamber 46, and ultimately from source chamber 70, equalto the difference in volume occupied by the piston rod 44 within thereload chamber 46, when the piston 40 is in the lowermost position asshown in FIG. 14, less the volume it occupies within the reload chamber(if any) when the piston 40 has reached its uppermost position. Thetravel of the piston 40 is adjusted so the piston rod remains within theaperture 48 at the uppermost limit of travel of the piston 40 and pistonrod.

The pump apparatus described above can pump liquid from point 22 topoint 32 as described above. The apparatus can pump liquid against asignificant hydraulic head, such as experienced in pumping water fromthe bottom of a mine, without requiring a pump with a high hydraulichead output. This is because liquid in column 92 acts upwardly againstthe bottom of the piston 40 and assists the movement of the piston 104towards the left, from the point of view of FIG. 14. When the piston 40is moved downwardly by the weight of liquid in cylinder 26 above thepiston, it moves the liquid in chamber 90 upwardly, increasing itshydraulic head and building up its potential energy. Thus a largeportion of the energy lost as the piston 40 moved downwardly isrecovered in potential energy represented by the liquid in column 92extending to cylinder 102.

Thus it may be seen that the cylinder 102 should be placed as high aspossible for the maximum recovery of the energy. It should be understoodthat the position of cylinder 102 could be different than shown in FIG.14. It could be, for example, oriented vertically. The terms “left” and“right” used above in relation to the cylinder, piston and piston rodassist in understanding the invention and are not intended to cover allpossible orientations of the invention. In some embodiments, thecomponents may be oriented vertically, horizontally, or any angledposition therebetween. For example, the components may be angled about5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85degrees or any number therebetween.

FIG. 15 shows a pumping apparatus 20.1 generally similar to theapparatus shown in FIG. 14 with like parts having like numbers with theaddition of “0.1”. It is herein described only regarding the differencesbetween the two embodiments. Only the upper portion of the apparatus isshown, the reload chamber and source chamber being omitted because theyare identical to the first embodiment. In this example passageway 34.1is fitted with a one-way valve 120 which permits liquid to flow fromchamber 90.1 into conduit 122, but prevents liquid from flowing in theopposite direction. The conduit 122 is connected to a receiver 124 whichmay be similar in structure to a hydraulic accumulator, for example, andcan store pressurized hydraulic fluid. When the piston 40.1 is moveddownwardly by the liquid in cylinder 26.1, it is forced into thereceiver 124.

A hydraulic conduit 126 connects the receiver to a centrifugal pump 128,which is connected to passageway 130 in the cylinder 26.1 below thepiston 40.1 via a conduit 132. After the piston reaches its bottommostposition, as shown in FIG. 15, pump 128 starts to pump liquid from thereceiver 124 into the chamber 90.1 to lift the piston 40.1. The factthat the liquid in the receiver 124 was pressurized during the previousdownward movement of piston 40.1 reduces the work required from pump 128to assist in raising the piston. This apparatus operates in a manneranalogous to the embodiment of FIG. 14, but uses the receiver to storepressurized hydraulic fluid instead of utilizing a physical, verticalhydraulic head as in the previous embodiment. Furthermore a centrifugalpump 128 is employed instead of the piston pump comprising cylinder 102and piston 104 of the previous embodiment. Otherwise this apparatusoperates in a similar manner.

Analysis of Pressures and Force Balance

Referring to FIGS. 14-19:

A₁ is the area of the top 29 of the transfer piston 40 which is the areaof the transfer cylinder 26

A₂ is the area of the bottom of the piston rod 42

A₁−A₂ is the area of the transfer piston in contact with the power fluid

S is the stroke length

P₁ is the pressure of the standing column

P₂ is the pressure of the working fluid during the power stroke

P₃ is the available head of the fluid to be pumped

P₄ is the pressure in the transfer chamber

P₅ is the pressure of the power fluid during the recovery stroke

P_(c) is the pressure created in the power cylinder 102 located at thesame level as the standing column discharge 32

W is the weight of the piston

R is the resistance created by the seals

d is the density of water (0.036 lbs/in³)

A_(c) is the area of the Power Cylinder

S_(c) is the stroke of the Power Cylinder

H is the height of the standing column of water d is the density ofwater

During the recovery stroke the transfer piston moves down, with valvemember 43 open and valve 56 closed.

Downward Forces F_(d)=P₁A₁+W

Upward Forces F_(u)=P₂(A₁−A₂)+P₄A₂+R

Net force F=F_(d)−F_(u)=P₁A₁+W−P₂(A₁−A₂)−P₄A₂−R

If we assume:

P₁=45 psig, approximately 100 feet of water, and A₁=8 in²,

P₁A₁=45×8=360 lbs

-   -   a piston weight of 2 lbs (approximately 8 in³ of steel)    -   a seal resistance 20 lbs    -   P₄=P₁ and therefore P₄A₂=P₁A₂

F=P₁A₁−P₁A₂−P₅(A₁−A₂)−R

F=P₁(A₁−A₂)−P₅(A₁−A₂)−R=(P₁−P.su−b.5)(A₁−A₂)−R

For this to be a net downward force, P₅ must be less than P₁. The areathat P₁ operates on is (A₁−A₂).

During the power stroke the transfer piston moves up and valve member 43closed.

Downward forces F_(d)=P₁A₁+W+R

Upward forces F_(u)=P₂(A₁−A₂)+P₄A₂

Net force=F=F_(u)−F_(d)=P₂(A₁−A₂)+P₄A₂−P₁A₁−W−R

P₄=P₃. If we assume P₃<<P or P₂, we can ignore P₄A₂.

As for the recovery stroke we can ignore W.

F=P₂(A₁−A₂)−P₁A₁−R

Efficiency

Work in During the Recovery Stroke

P₅=P₁−P_(c) where P_(c) is the pressure created in the power cylinderlocated at the same level as the standing column discharge.

Work Done at the Power Cylinder

W_(i)=P_(c)A_(c)S_(c),

A_(c)S_(c) is the volume of power fluid moved per stroke=(A₁−A₂)SW_(i)=P_(c)(A₁−A₂)S,

For an example, P_(c)=14 psig, A₁=8 in² ₁A₂=4 in² ₁ and S=12 in

W₁=14(8−4)12=672 in lbs (56 ft lbs) plus R×S 20×12=240 in lbs. A₂/A₁=0.5

Work in During the Power Stroke

P₂=P₁+P_(c). To create an acceleration of “a” times g (32.2 ft/sec²) inthe standing column, the net force must be “a” times the weight of thestanding column.

F=P₂(A₁−A₂)−P₁A₁−R=aHA₁d=aP₁A₁

(P₁+P_(c))(A₁−A₂)−P₁A₁−R=aP₁A₁

P₁A₁−P₁A₂+P_(c)A₁−P₁A₂−P.su−b.1A₁−R=aP₁A₁. The bold terms cancel.

P_(c)(A₁ − A₂) = aP₁A₁ + P₁A₂ + R$P_{c} = {\frac{P_{1}( {{aA}_{1} + A_{2}} )}{( {A_{1} - A_{2}} )} + \frac{R}{( {A_{1} - A_{2}} )}}$

For a head of 100 feet, P₁=43.3 psig, and a=1 g, R=20 lbs.

$P_{c} = {{\frac{43.3( {{1 \times 8} + 4} )}{4} + \frac{20}{4}} = {{130 + 5} = {135\mspace{14mu} {psig}}}}$

Work in at the Power Cylinder

W_(i)=P_(c)(A₁−A₂)S=135×4×12=6480 in lbs

Work Output

The water lifted is SA₂d=12×4×0.036=1.73 lbs and it is raised 1200inches.

W₀=1/73×1200=2070 in lbs=173 ft lbs

Efficiency based on A₂/A₁ ratio of 0.5

E=W₀/W₁=2070/(6480+672+240)=28.0%

By examining the above formula for P_(c) one can see how changing theacceleration and the ratio of A₂/A₁ affects the pressure necessary todrive the pump. For example:

A₂/A₁=0.8 or in the example A₂ would now=6.4 sq. in. and a=0.25 g

$\begin{matrix}{P_{c} = {\frac{P_{1}( {{aA}_{1} + A_{2}} )}{( {A_{1} - A_{2}} )} + \frac{R}{( {A_{1} - A_{2}} )}}} \\{P_{c} = {\frac{43.3( {{{.25} \times 8} + 6.4} )}{1.6} + \frac{20}{1.6}}} \\{= {227 + 12.5}} \\{= {239.5\mspace{14mu} {psig}}}\end{matrix}$

or using a lower A₂/A₁ ratio—say 0.25, now A₂=2 and leaving accelerationat 0.25 g

$\begin{matrix}{P_{c} = {\frac{P_{1}( {{aA}_{1} + A_{2}} )}{( {A_{1} - A_{2}} )} + \frac{R}{( {A_{1} - A_{2}} )}}} \\{P_{c} = {\frac{43.3( {{{.25} \times 8} + 2} )}{6.6} + 20}} \\{= {28 + 3.33}} \\{= {31.33\mspace{11mu} {psig}}}\end{matrix}$

We are now moving a volume of water up 100 feet in our example by adding31.33 psi (72.37 ft.) of head to the power column.

Dynamic Analysis of the Original Concept

Recovery Stroke

Continuing with the same example the net force on the Standing Column 26is: F=P_(c)(A₁−A₂)−R=14(8−4)−20=36 lbs

The mass of the Standing Column is

1200×8×0.036=346 lbs.

The acceleration is

36/346=0.10 g=3.22 ft/sec²

The time required to complete the stroke

${D = \frac{{at}^{2}}{2}};{D = {{S\mspace{14mu} {in}\mspace{14mu} {feet}} = {1\mspace{14mu} {foot}}}};$t = (2S/a)^(0.5) = (2/3.22)^(0.5) = 0.79  seconds

Power Stroke

The acceleration was defined as 1 g or 32.2 ft/sec².

t=(2/32.2)^(0.5)=0.25 seconds.

The complete stroke will take 0.79+0.25=1.03 seconds

The above analysis of pressures and force can be manipulated usingdifferent ratios of A₂/A₁, P₂/P₁ and acceleration “a”.

Attached as FIG. 16 is a performance curve for the pressure head conceptshowing the efficiency against the ratio A₂/A₁. Also included as Table24 are the calculations from which FIG. 16 is drawn showing the absolutenumeric variations as parameters are changed.

TABLE 24 Efficiency vs. A2/A1 A2/A1 = P2/P1 0.4 0.5 0.6 0.7 0.8 0.82 1.50.0% 0.0% 0.0% 0.0% 0.0% 0.0% 1.8 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 2.041.4% 0.0% 0.0% 0.0% 0.0% 0.0% 2.5 31.6% 45.7% 0.0% 0.0% 0.0% 0.0% 3.025.5% 37.2% 53.3% 0.0% 0.0% 0.0% 4.0 18.5% 27.1% 39.3% 59.1% 0.0% 0.0%5.0 14.5% 21.3% 31.2% 47.1% 0.0% 0.0% 7.5 9.4% 13.9% 20.5% 31.3% 53.7%61.1% 10 6.9% 10.3% 15.3% 23.5% 40.2% 45.8% optimum 26.6% 315.% 36.0%40.7% 46.3% 47.5% P5/P1, req 0.39 0.31 0.185 0.05 0.05 0.05 Rec Accft/sec² 8.04 8.01 8.04 7.21 4.21 3.61 P2/P1 opt 2.9 3.48 4.35 5.79 8.699.65

For the pressure head concept, the curves demonstrate that a pump couldapproach an efficiency of up to 61% if used in applications where a highpressure head is available and the power water can be discharged at alow level, both compared to the height of the standing column. Efficientpump designs have a high A₂/A₁ ratio indicating the volume of waterdischarged from the standing column is greater than the volume of waterused on the power side of the transfer piston. This feature indicatesthat the pump may be attractive in lifting water from a well orde-watering a mine if there is a convenient source of suitable powerwater; i.e. compatible with the water to be lifted and having a highhead. As previously discussed, a pressure head pump could be attractivein some run-of-the-river hydro applications if a suitable source ofpower water is convenient.

For the power cylinder concept, the curves indicate that the higher theA₂/A₁ ratio the more efficient the pump, and the lower the accelerationsthe more efficient the pump.

Efficient pressure head concept pumps move a greater volume of processwater per stroke than the volume of power water required. This againresults directly from the high ratios of A₂/A₁. This means that thepower water could be released to join the process water and still alloweffective pumping to occur. Conversely, pumps with low ratios of A₂/A₁but with a large amount of power water and a lower head can move smalleramounts of process water up greater heights. They will expend more powerwater than the process water they move. This process is similar to theclassic hydraulic ram principle where a large amount of fluid at a lowpressure head is used to transfer a small amount of fluid up a higherelevation.

A different embodiment of the pump utilizes a bladder similar to apressure tank in a water system or a packer similar to a drill holepacker that houses the water in the power cylinder pressurized by air orhydraulic pressure and then the pressure lowered and againre-pressurized. This allows the use of the pump without expending thepower fluid.

Analysis

FIG. 17 shows the two main embodiments of the pump. FIG. 18A describesthe pressure head concept showing how the liquid, generally water,stored at a higher elevation 83 supplies excess pressure for the powerstroke 85 and reduced pressure 87 when point 89 is used for the powerfluid release. FIG. 18B shows the power cylinder concept where theexcess pressure is generated by the power cylinder 102 and the recoverystroke is augmented by the creation of a vacuum when piston 104 iswithdrawn from the column of power fluid.

Performance Curves

Pressure Head Concept

Referring to Table 24, the valves were manipulated to calculate theefficiency of various pressure head arrangements. The manipulationrequired:

setting various ratios of A₂/A₁ from 0.4 to 0.82 then, for each of theratios,

calculating the recovery stroke performance for various ratios of P₅/P₁(the height of the power water release compared to the standing columnheight),

“optimising” P₅/P₁ to obtain a recovery stroke acceleration of 8ft/sec², if possible,

using the “optimised” results from the recovery stroke calculations asinput for the power stroke calculations,

calculating the power stroke performance for various ratios of P₂/P₁(the height of the power water source compared to the standing columnheight),

“optimising” P₂/P₁ was to obtain a power stroke acceleration of 8ft/sec²,

transferring the calculated efficiencies to another spreadsheet alongwith the “optimised” P₅/P₁ and P₂/P₁ ratios and the recovery strokeacceleration,

using the calculated efficiencies to plot a graph of efficiency vs.A₂/A₁ for the most significant ratios of P₂/P₁.

The results indicated that high ratios of A₂/A₁ result in higherefficiency and low acceleration. The results also indicate that a lowratio of P₅/P₁ is required to create reasonable recovery strokeacceleration.

Referring to Table 24, performance data for the ratio A₂/A₁=0.82 isshown which indicates that an efficiency of 61% could be achieved if apower stroke acceleration of 8 ft. sec 2 (0.25 g) is consideredacceptable. The recovery stroke acceleration will be around 4 ft/sec2with this design.

What is not immediately apparent is that when the A₂/A₁ ratio is high,the power water released per stroke is much less than the process waterlifted per stroke. The process water lifted per stroke is A₂ S and thepower water released per stroke is (A₂−A₁)S.

When A₂/A₁=0.8:

(A₂−A₁)=A₁−0.8 A₁=0.2A₁

and the amount of power water released per stroke is

(A₂−A₁)S=0.2 A₁S

and A₂=0.8 A₁:

therefore the amount of process water lifted is

A₂S=0.8 A₁S

or four times the amount of power water released.

This means that the power water could be released into the process waterand the pump will still pump a net of (0.8−0.2)A₁S=0.6 A₁S per stroke.

Power Cylinder Concept

Values were manipulated to calculate the efficiency for various powercylinder arrangements. The manipulation required is:

setting various ratios of A₂/A₁; from 0.4 to 0.82, then, for each of theratios,

setting the pressure in the power cylinder (P_(c)) during the recoverystroke,

calculating the recovery stroke performance for various ratios ofH_(p)/H₁ (the height of the pump compared to the height of the standingcolumn),

“optimising” H_(p)/H₁ to obtain a recovery stroke acceleration of 8ft/sec², if possible,

using the “optimised” results from the recovery stroke calculations asinput for the power stroke calculations,

calculating the power stroke performance for various ratios of P₂/P₁,

“optimising” P₂/P₁ to obtain a power stroke acceleration of 8 ft/sec²,

transferring the calculated efficiencies to another spreadsheet alongwith the “optimised” H_(p)/H₁ and P₂/P₁ ratios and the recovery strokeacceleration,

using the calculated efficiencies to plot a graph of efficiency vs.A₂/A₁ for the most significant ratios of P₂/P₁.

The results indicate that high ratios of A₂/A₁ result in higherefficiency and lower ratios allow moving fluid to higher heads but usingmore process water or a larger power column if contained in a bladder orpacker.

Applications

For the concept pump to be reasonably efficient, the ratio A₂/A₁ must behigh. For this sort of pump to have a reasonable recovery strokeacceleration the power water in a pressure head style pump must bereleased low relative to the height of the standing column. For thissort of pump to have a reasonable power stroke acceleration the powercolumn must be tall relative to the standing column. These featuresindicate that the pump would be attractive in applications where thereis a source of power water at an elevation much higher than the standingcolumn height. It must also be possible to release the power water at alow elevation relative to the height of the power column in a pressurehead style pump.

The previously discussed run-of-the-river hydro booster applicationcould fit these requirements, Analysis shows this application allows therecovery of more than 55% of the energy of a high elevation tributary ifit is channeled to a pressure head style pump placed at the bottom. Thepump lifts almost five times as much water as is used to power the pumpif the water is lifted 1/10^(th) of the height of the power head. Thewater is then recycled through the turbine at the bottom. Using the pumpto de-water a mine could also be attractive. Raising water from a wellcould be attractive. Raising water to a reservoir or to a higherelevation (pressure) could also be attractive

Another embodiment of the present invention is illustrated in FIG. 19Aand FIG. 19B, wherein like parts have like reference numerals with theadditional suffix “0.2”. Referring first to FIG. 19A, a piston typepumping apparatus is shown indicated by reference numeral 20.2. Theapparatus is intended to pump liquids, typically water, up relativelygreat vertical distances as exemplified by the distance between points22.2 and 24.2.

There is a vertically oriented cylinder 26.2 having a top 28.2 and abottom 30.2. A piston 40.2 is reciprocatingly mounted within thecylinder 26.2 and is connected to a vertically oriented, hollow pistonrod 42.2 which extends slidably and sealingly through aperture 44.2 inthe top 28.2 of the cylinder and aperture 48.2 in the bottom 30.2 of thecylinder. The piston 40.2 is annular in shape, in this example, has asurface area 41.2 and divides the cylinder into two sections exemplifiedby cylinder space 27 below the piston and cylinder space 31 above thepiston. The cylinder 26.2 has a diameter D_(C) and the hollow piston rod42.2 has a diameter D_(PR).

The piston rod 42.2 has a first portion 218 below the piston 40.2 and asecond portion 220 above the piston. The first portion 218 extendsslidably and sealingly through the aperture 48.2 and the second portion220 extends slidably and sealingly through the aperture 44.2. It shouldbe understood that FIG. 19A and FIG. 19B are simplified drawings of theinvention and seals and other conventional elements which would beapparent to someone skilled in the art are omitted.

There is a first one-way valve, indicated by reference numeral 41.2, attop 50 of the piston rod 42.2. Valve 41.2 has a valve member 43.2 and avalve seat 45.2 which extends about a first passageway 47.2 in the top50 of the piston rod 42.2.

There is a reload chamber 46.2 adjacent bottom 30.2 of the cylinder 26.2and is sealed with the cylinder apart from the aperture 48.2. The reloadchamber 46.2 is in the form of a cylinder, in this example, and has adiameter D_(RL). A second one-way valve indicated by reference numeral56.2 is located at a bottom 57 of the reload chamber 46.2 and includes avalve member 58.2 and a valve seat 60.2 which extends about a secondpassageway 52.2 in the bottom of the reload chamber.

The second one-way valve allows liquid to flow from a source of liquidto be pumped below the apparatus 20.2 into the reload chamber 46.2 andinto hollow piston rod 42.2, but prevents liquid from flowing from thereload chamber towards the source below.

There is a transfer chamber 200 adjacent the top 28.2 of the cylinder26.2 and is sealed with the cylinder apart from the aperture 44.2. Thetransfer chamber 200 is in the form of a cylinder, in this example, andhas a diameter D_(TC). The second portion 220 of the piston rod 42.2acts as a piston within the transfer chamber 200. There could be apiston member on the end of the piston rod 42.2 within the transferchamber 200 and the term “piston rod” includes this possibility.

The first one-way valve 41.2 allows liquid to flow into the transferchamber 200 from the hollow piston rod 42.2 and from the reload chamber46.2, but prevents a reverse flow into the hollow piston rod and reloadchamber.

Since the transfer chamber 200 and the reload chamber 46.2 are above andbelow the cylinder 26.2 respectively, in this embodiment, the cylinderdiameter D_(C) can be sized such that the piston rod diameter D_(PR) canbe equal to or less than the diameters D_(TR) and D_(RL) of the transferchamber 200 and reload chamber 46.2 respectively, and can also be sizedsuch that the surface area 41.2 of the piston 40.2 is large enough foroptimal pumping. The larger the diameter D_(PR) of the piston rod 42.2,the greater the volume of fluid that can be pumped by the apparatus20.2. The greater the surface area 41.2 of the piston 40.2 the greaterthe pumping force.

A third one-way valve indicated by reference numeral 202 is located atthe top 204 of the transfer chamber 200 and includes a valve member 206and a valve seat 208 which extends about a third passageway 210 in thetop of the transfer chamber. There is a discharge chamber 212 above andadjacent to the transfer chamber 200 and is sealed with the transferchamber apart from the third one-way valve 202. The third one-way valve202 allows liquid to flow from the transfer chamber 200 into thedischarge chamber 212, but prevents a reverse flow of liquid from thedischarge chamber into the transfer chamber.

A fourth passageway 214 is located in the bottom 30.2 of the cylinder26.2 and a fifth passageway 216 is located in the top 28.2 of thecylinder. The fourth and fifth passageways 214 and 216 allow a flow ofpressurized liquid into and out of the cylinder spaces 31 and 27respectively as explained below. Typically, the fourth and fifthpassageways 214 and 216 respectively would be connected to a source ofpressurized liquid via respective conduits and respective valves.

In operation, the apparatus 20.2 is primed by filling the reload chamber46.2, the hollow piston rod 42.2 and the discharge chamber 200 withfluid, typically water, and the piston is placed in its lowermostposition next to bottom 30.2 of cylinder 26.2. The first, second andthird one-way valves 41.2, 56.2 and 202 are closed.

During the power stroke, shown in FIG. FIG. 19A, pressurized fluid islet into the cylinder space 27 through passageway 214. The pressurizedfluid acts on the piston 40.2, causing it to rise from the bottom 30.2towards the top 28.2.

The second portion 220 of the piston rod 42.2 rises upwardly through theaperture 44.2 and thereby creates an increased pressure in the transferchamber 200 since the volume of space occupied by the second portion inthe transfer chamber is increased.

The increased pressure in the transfer chamber 200 causes the valvemember 43.2 of the first one-way valve 41.2 to remain firmly seated inits valve seat 45.2, such that liquid is prevented from flowing throughpassageway 47.2. The increased pressure also causes the valve member 206of the third one-way valve 202 to rise off its seat 208, such thatliquid may flow from the transfer chamber 200 into the discharge chamber212.

The volume of liquid flowing from the transfer chamber 200 into thedischarge chamber 212 is substantially equal to the increased volumeoccupied by the second portion 220 of the piston rod 42.2 in thetransfer chamber.

Correspondingly, the first portion 218 of the piston rod 42.2 risesupwardly through the aperture 48.2, increasing the volume of spaceoccupied by the reload chamber 46.2 and the hollow piston rod 42.2combined. Since the first one-way valve 43.2 is closed, as discussedabove, the pressure in the reload chamber 46.2 and in the hollow pistonrod 42.2 is reduced.

The reduced pressure in the reload chamber 46.2 causes the valve member58.2 of the second one-way valve 56.2 to rise off its seat 60.2, suchthat liquid flows from the source below into the reload chamber throughpassageway 52.2. The volume of liquid flowing from the source into thereload chamber 46.2 is substantially equal to the increase in totalvolume occupied by the hollow piston rod 42.2 and the reload chamber46.2 combined, such that the pressure is equalized between the source,the reload chamber and the hollow piston rod.

During the power stroke the piston 40.2 continues to travel until itreaches the top 28.2 of the cylinder 26.2. The increase in the totalvolume of space occupied by the hollow piston rod 42.2 and the reloadchamber 46.2 is equal to the decrease of volume occupied by fluid in thetransfer chamber 200. The decrease in volume of fluid in transferchamber 200 is equal to increase in the volume of space occupied by thesecond portion 220 of the piston rod in the transfer chamber 200.

Referring now to FIG. 19B, during the recovery stroke pressurized fluidis let into the cylinder space 31 through passageway 216. Thepressurized fluid acts on the piston 40.2 such that it is deflecteddownwards from the top 28.2 of cylinder 26.2 towards the bottom 30.2.Simultaneously, pressurized fluid from space 27 is released throughpassageway 214.

Initially during the recovery stroke, with the first one-way valve 41.2closed and the third one-way valve 202 open, the pressure in thetransfer chamber 200 is decreased since the volume of space occupied bythe second portion 220 of the piston rod 42.2 is decreased. Thisdecrease in pressure causes the valve member 206 of the third one-wayvalve 202 to seat itself on seat 208 which thereby prevents any fluidfrom the discharge chamber 212 from flowing through passageway 210 intothe transfer chamber 200.

Similarly, during the initial period of the recovery stroke with thefirst one-way valve 41.2 closed and the second one-way valve 56.2 open,the pressure in the reload chamber 46.2 is increased since the totalvolume of space occupied by the piston rod 42.2 and the reload chamberis decreased while the volume of fluid therein remains at firstconstant. This increased pressure causes the valve member 58.2 of thesecond one-way valve 56.2 to seat itself on seat 60.2 which therebyprevents any fluid from the reload chamber 46.2 and the hollow pistonrod 42.2 from flowing through passageway 52.2 into the source.

Once the second one-way valve 56.2 closes, the total volume of fluid inthe space defined by the reload chamber 46.2, the hollow piston rod 42.2and the transfer chamber 200 remains constant. During this period of therecovery stroke, with the first one-way valve 41.2, the second one-wayvalve 56.2 and the third one-way valve 202 closed, the volume of spaceoccupied by the second portion 220 of the piston rod 42.2 in thetransfer chamber 200 is reduced as the piston 40.2 travels towards thebottom 30.2 of cylinder 26.2 which causes a reduced pressure in thetransfer chamber. A simultaneous increase in pressure occurs in thevolume of space contained within the reload chamber 46.2 and the hollowpiston rod 42.2.

The decrease in pressure in the transfer chamber 200 and increase inpressure in the hollow piston rod 42.2 and the reload chamber 46.2causes the valve member 43.2 to rise off its seat 45.2, allowing thefluid to flow from the reload chamber and hollow piston rod into thetransfer chamber to equalize the pressure.

The recovery stroke ends with the piston 40.2 next to bottom 30.2 ofcylinder 26.2 and with the transfer chamber 200, the hollow piston rod42.2 and the reload chamber 46.2 filled with liquid. The apparatus 20.2is then ready for another power stroke. This cycle of a power strokefollowed by a recovery stroke is alternately repeated during theoperation of the apparatus 20.2.

An advantage of the present embodiment is obtained by the novel use ofthe third one-way valve 202 which prevents liquid in the dischargechamber 212 from reentering the transfer chamber 200 during the recoverystroke. This improves the efficiency of the pump significantly sinceenergy is not wasted re-pumping the same liquid.

Another advantage is due to the configuration of the reload chamber46.2, the cylinder 26.2 and the transfer chamber 200. This configurationallows the piston rod diameter D_(PR) to be equal to or less than thediameters D_(RL) and D_(TC) of the reload chamber and transfer chamberrespectively. The greater the piston rod diameter D_(PR), the greaterthe volume of fluid that can be pumped by the apparatus 20.2.Furthermore, since the diameter D_(C) of the cylinder 26.2 is not boundby either the reload chamber 46.2 or the transfer chamber 200, thesurface area 41.2 of the piston 40.2 can be made as large as necessaryfor an optimal pumping force. The greater the surface area 41.2 of thepiston 40.2, the greater the force of the piston rod 42.2 acting on thewater in the transfer chamber 200 for a given pressurized fluid on thepiston through passageway 214.

Accumulator

Performance of a downhole pump with a given A1/A2 ratio can be improvedthrough the use of an accumulator and a pressure-maintaining valve inthe produced fluid conduit at the surface. An accumulator is a pressurestorage reservoir in which a non-compressible fluid is held underpressure by an external source. The external source can be a spring, araised weight, or a compressed gas. An accumulator enables the system tocope with extremes of demand using a less powerful pump, to respond morequickly to a temporary demand, and to smooth out pulsations. It is atype of energy storage device. FIG. 25 depicts a system utilizing anaccumulator with a Hygr Fluid System pump. The system includes a powersource, e.g., solar power, a hydraulic drive, an accumulator drive, aHygr Fluid System downhole pump, and a pump discharge. FIG. 26 depicts asystem utilizing an accumulator drive and recycle system with a HygrFluid System pump. depicts a system utilizing an accumulator with a HygrFluid System pump. The accumulator includes a power source, e.g., solarpower, a hydraulic drive, an accumulator drive, a Hygr Fluid Systemdownhole pump, an accumulator recycle, and a pump discharge.

Various types of accumulators are suitable for use in the preferredembodiments. One of the simplest types of accumulators is the toweraccumulator, wherein water is pumped to a tank and the hydrostatic headof the water's height above that of the pump provides pressure. A raisedweight accumulator includes a vertical cylinder containing fluidconnected to the fluid conduit. The cylinder is closed by a piston onwhich a series of weights are placed that exert a downward force on thepiston and thereby energizes the fluid in the cylinder. In contrast tocompressed gas and spring accumulators, this type delivers a nearlyconstant pressure, regardless of the volume of fluid in the cylinder,until it is empty.

A compressed gas accumulator includes a cylinder with two chambersseparated by an elastic diaphragm, a totally enclosed bladder, or afloating piston. One chamber contains fluid and is connected to thefluid line. The other chamber contains an inert gas under pressure(typically air, nitrogen or other gas) that provides the compressiveforce on the fluid. Inert gas is typically preferred to avoid combustionof oxygen and oil mixtures in the system under high pressure. As thevolume of the compressed gas changes, the pressure of the gas (and thepressure on the fluid) changes inversely. The open loop accumulatorworks by drawing air in from the atmosphere and expelling air into theatmosphere. A separate pump maintains the pressure balance of the air byincreasing the fluid in the system. This results in a steady pressure ofair and up to 24 times the energy density of a standard hydraulicaccumulator.

A spring type accumulator is similar in operation to the gas-chargedaccumulator, except that a heavy spring (or springs) is used to providethe compressive force. According to Hooke's law the magnitude of theforce exerted by a spring is linearly proportional to its extension.Therefore as the spring compresses, the force it exerts on the fluid isincreased linearly. The metal bellows accumulators function similarly tothe compressed gas type, except the elastic diaphragm or floating pistonis replaced by a hermetically sealed welded metal bellows. Fluid may beinternal or external to the bellows. The advantages to the metal bellowstype include exceptionally low spring rate, allowing the gas charge todo all the work with little change in pressure from full to empty, and along stroke relative to solid (empty) height, which gives maximumstorage volume for a container size. The welded metal bellowsaccumulator provides an exceptionally high level of accumulatorperformance, and can be produced with a broad spectrum of alloysresulting in a broad range of fluid compatibility. Another advantage tothis type is that it does not face issues with high pressure operation,thus allowing more energy storage capacity. There may be more than oneaccumulator, or type of accumulator, employed in the systems ofpreferred embodiments.

In operation, an accumulator is placed close to the pump with anon-return valve preventing flow back to the pump. In the case ofpiston-type pumps this accumulator is placed in a location to absorbpulsations of energy from a multi-piston pump. It also helps protect thesystem from fluid hammer. This protects system components, particularlypipework, from both potentially destructive forces. An additionalbenefit is the additional energy that can be stored while the pump issubject to low demand, enabling use of a smaller-capacity pump.Accumulators are often placed close to the demand to help overcomerestrictions and drag from long pipework runs. The outflow of energyfrom a discharging accumulator is much greater, for a short time, thaneven large pumps could generate. An accumulator can maintain thepressure in a system for periods when there are slight leaks without thepump being cycled on and off constantly. When temperature changes causepressure excursions the accumulator helps absorb them. Its size helpsabsorb fluid that might otherwise be locked in a small fixed system withno room for expansion due to valve arrangement. The gas precharge incertain accumulator designs is typically set so that the separatingbladder, diaphragm or piston does not reach or strike either end of theoperating cylinder. The design precharge normally ensures that themoving parts do not foul the ends or block fluid passages.

The use of an accumulator may increase the rate at which the downholepiston is reset, thereby increasing the productivity of the downholepump. Use of an accumulator may also ensure sufficient force over andabove that created by the fluid head is available to reset the downholepiston if/when the fluid head alone is insufficient.

An alternate pump drive method may involve using a transfer barrieraccumulator and control valve in the produced fluid conduit at thesurface. Using the hydraulic drive pump to alternate pressure on thepower column and produced fluid column (via the transfer barrieraccumulator) may increase the rate at which the downhole pump may bestroked by enabling the controlled timing of both alternating pressures,thereby increasing the productivity of the downhole pump. By allowingfor the introduction of additional force over and above that created bythe fluid head, and/or what may be practically achieved with anaccumulator and pressure-maintaining valve, the A1/A2 ratio may bedecreased, thereby enabling the downhole pump to operate at deeperdepths without increasing the power fluid pressure at the surface.

In one embodiment, an accumulator drive system is provided wherein asurface hydraulic accumulator is powered up by a pump on the surface.The pump can any type and can be powered by electricity, solar, or wind,or through the hydraulic ram principle as described herein, or by hand.Once the desired pressure is reached, the downhole pump strokes pumpingliquid to the surface. The downhole pump can be situated in any desiredconfiguration, e.g., vertical, horizontal, or at any angle therebetween.In one embodiment, a hydraulic impulse is used to power the downholepump (“the Hygr Fluid System”). In this embodiment, the drive pipehydraulic line can be any length or angle, as the flow of hydraulicfluid (e.g., water, oil or other liquid) is not impeded by angles,curves or changes in depth or altitude.

An accumulator reset can be employed in systems of certain embodiments.Such accumulator reset systems are desirable for use in connection withdownhole systems, e.g., water wells where a standard water pressure tankis used. Hydraulic accumulators are typically preferred for their higherpressure and deeper pump settings. In operation, an accumulator on thesurface has its pressure raised by the downhole pump as it deliversfluid from the well. This extra pressure helps push the transfer pistonin the pump down on the reload cycle. In a preferred embodiment, thepump utilizes a larger piston area at the top of the transfer pistonexert sufficient force to push the piston back down to reload; however,sometimes gas in the fluid and/or gas and oil wells keeps the fluid inthe lines lighter than the drive fluid in the other hydraulic line.Extra force may then be necessary to push the piston down. Besidesproviding downward force on the transfer piston, use of a hydraulicaccumulator also helps to regulate the pumping cycles. A timer can beemployed to in connection with the accumulator to assist in improvingpump function.

In certain embodiments, using the Accumulator Drive and Reset eliminatesthe need to drive the downhole pump with a Continuous Hydraulic DriveUnit (CHDU) on the Drive side. Instead, an Accumulator can be placed onthe Drive side and pressurized by using a pump or an Acccumulator plus apump on the Delivery side of the system. The Delivery side can beoverpressurized from the Hydraulic Drive side and run through anAccumulator on the Delivery side with extra pressure to help reset theTransfer Piston in the downhole pump. By putting a pump on the Deliveryside, one can degas the liquid from a well and then add whateverpressure is necessary to reset the Transfer Piston and pressurize theAccumulator on the Drive Side. That Accumulator will have a presentpressure that is great enough to stroke the downhole pump and producefluid out the Delivery line. With the Hygr Fluid System, there isconstant transfer of the energy from one state to another to drive thepumping system, with a small amount added when necessary to replace theenergy transferred to friction losses.

The systems are particularly suited for water pumping applications, butare also applicable to oil and gas applications. Gas wells all loseproduction due to liquid buildup in the well as the formation pressuredecreases. When the wells are deliquified (dewatered) the resultingfluid has some entrained gas. By resetting the downhole Transfer Pistonfrom the Delivery side, one can run the produced fluid through adegassing system and then run it to an Accumulator and have a pump thatis powered by electricity, solar or gas as with the Blair system or gaspowered systems that will pressurize a very large Accumulator or aSurface Drive pump can be put on the Delivery side to pressurize thesystem.

In one embodiment of a multi-pump system, the Hygr Fluid System can beadapted so one central drive unit powers multiple downhole pumps. Thehydraulic pump system can operate with the hydraulic line in ahorizontal, vertical, or angled position, such that the drive unit canbe placed in the middle, or side of several pumps. This lends itselfwell to the pumping of oil or gas wells in close proximity. Instead ofhaving a pump and drive unit on each well, the central drive unit can betimed to turn individual pump(s) on or off as desired. This allows onepump to be working permanently while other pumps are turned on or off ona selected basis, or all pumps can be sequentially or intermittentlyoperated for continuous or discontinuous operation. For the gas and oilmarket this offers improved costing, safety and environmentalreliability. The Hygr Fluid System is particularly well-suited to mine,excavation, and open pit dewatering.

In one embodiment, a driver using wellhead gas (“Blair Driver”) can beadapted to the Hygr fluid system and supply power to the system fromexisting gas production. This design is desirable for remote locations.The Blair Driver and Blair Drive System are described in U.S. Pat. No.6,065,387, U.S. Pat. No. 6,499,384, and Canada Pat. No. 2,276,868, thedisclosures of which are incorporated by reference herein in theirentireties.

For mine, excavation, and open pit dewatering, a pump can be employed inthe bottom of the pit that pumps water up about 50% of the way out ofthe pit, then transfers it to a second pump that lifts the water therest of the way out of the pit (FIG. 20). With the Hygr Fluid system,the bottom pump is powered with the hydraulic force (energy) of thewater column from the top of the excavation. The Hydraulic Ram principlepowers the bottom Hygr fluid system unit and pumps the water 50% or moreout of the pit and then a regular pump using standard electric powerthen pumps the fluid the rest of the way out of the pit. This systemthen uses at least 50% less purchased electric power to pump the liquidout of the pit than would be used by a conventional system, therebyreducing the cost of energy for operating the system by 50% or more.

Energy conversion is depicted in FIG. 21. Water at a higher level isdirected straight to the pump and powers the pump stroke. This avoidsrunning the water through a generator to generate electricity, which istransported via power lines to the surface and then back down to thepump, resulting in substantial energy savings.

In one embodiment, the hydraulic cylinder on the surface moves forwardand produces a hydraulic impulse transmitted through the delivery pipeto the pump. The delivery pipe (Drive Line) operates on hydraulicimpulse, and can be in any desired configuration, e.g., horizontal,vertical, on an angle or a corkscrew.

It has been observed that use of water as a hydraulic fluid to power thedownhole pump exhibits some compression at 1000 ft., with thiscompression effect becoming more pronounced at 1500, 2000, 3000, 4000,6000, or 10,000 ft. A Continuous Hydraulic Drive System has beendeveloped to address this issue. In this system, as much fluid is pumpedon the surface as needed to account for the hydraulic compression of theDrive Fluid plus what is necessary to drive the pump. As an example ofthis compression effect in operation, if 1 gallon is pumped with a driveunit on the surface, 1 gallon is obtained from the pump. When the pumpwas set to operate at a depth of 1600 ft., if 1 gallon is pumped withthe drive unit on the surface, only ½ gallon is obtained from the pump.

The use of an accumulator can mitigate compression observed with asurface drive unit powering the downhole pump. An accumulator on thesurface can be powered by any low energy pumping system and once itgains enough pressure it can send a hydraulic impulse down the DriveString to the downhole pump and it makes a stroke. The power to drivethe low horsepower (e.g., ¼ HP) pump to pressurize the surfaceaccumulator can be solar, wind, hand, or any other desired energysource. The pump may only stroke once or twice an hour, as it may take along time to pressure up the surface accumulator—but the well only needs1 or 2 strokes an hour to keep the water pumped off and the gas flowing.

In FIG. 22 are shown two Hydraulic Accumulators, the one on the right ofthe Drive Unit is used to overpressurize the system to add energy to theRecovery (return) stroke. The one on the left is the Accumulator DriveSystem powered by electricity. The Accumulator gains in pressure, thensends and impulse down the line to power the pump. The system of FIG. 22is employed with a pump positioned down 200 ft., and the water comingfrom the hose is from 200 ft.

FIG. 23 shows a Drive Unit and a Control Unit. The Drive (Power) andControl units can easily and economically drive and control the systemsof preferred embodiments at any distance (even thousands of miles away).Electronic controls can power and monitor everything that is happening.FIG. 24A shows wells close together. One Drive Unit (FIG. 24B) can beplaced in the middle of the wells and drive all of them, instead ofhaving one drive unit on each well.

FIG. 27 shows the Blair Air System driving the Hygr Fluid Systemdownhole pump. The system was developed to use the pressure in a naturalgas line to run an air compressor and then re-inject the gas into thegas line. This supplies compressed air to a gas well to runinstrumentation and small pneumatic pumps and to achieve an emissionsfree well site. The system can be configured to provide power to thedownhole pump of preferred embodiments with reciprocating pumpingaction. The reciprocating action used to power the air system can bemodified to power a surface hydraulic pump as in certain embodiments.FIG. 27 depicts providing the oil to the Hygr pump. This is theHydraulic Fluid used to drive the downhole pump. FIG. 28 shows theProduced Water Tank. This is the water taken from the gas well todeliquify it. The system is particularly well-suited for dewatering (ordeliquification) of gas wells. Every gas well loses pressure over timeand the fluid (poor quality water) builds up and holds the gas in theformation. Gas producers initially finish wells with a 4½″ or largercasing. As the well loses pressure, a small tubing string—usually 2⅜′ or2⅞″ —is installed as a “Velocity String”. The same amount of gas thatwas going up the 4½″ or larger casing then goes up the tubing string ofsmaller cross-sectional area. This increases the velocity and carriesthe water out of the formation. Once the pressure drops further, aPlunger Lift is installed. This is a unit that falls to the bottom ofthe string when the pressure is low and holds the well shut until enoughpressure is built up to push it to the top of the well and to carry allthe fluid out. Once the pressure reduces further, the well is “swabbed”,which involves pushing a plunger down the well and drawing it back outto get the water out of the well bore. Often a Plunger Lift is notemployed—instead, swabbing is used.

With the Hygr Fluid System, a low cost pumping system can be installedat the beginning of the liquification cycle when the pressure dropsbelow the level necessary to keep the velocity high enough in the wellbore to carry the liquid out. Engines powered by natural gas are wellsuited to provide energy in certain embodiments, such as high producinggas wells. The systems can economically bring back into production lowproducing gas wells. Once the well is liquified and the well does notproduce gas it must be properly decommissioned and abandoned. Using theHygr Fluid System with the reconfigured Blair System (Hygr Blair Drive)enables such wells will continue to produce gas for a much longer timewith no emissions, offering substantial environmental benefits.

FIG. 29 is a block diagram depicting one embodiment of a Hygr FluidSystem. The system includes a recharge chamber with top piston A₁, atransfer chamber with bottom piston A₂, a transfer check valve, anintake check valve, a product water tank, and a fluid transfer line tothe drive unit. FIG. 30 is a block diagram depicting the power stroke ofthe depicted embodiment of the Hygr Fluid System of FIG. 29. Thetransfer check valve is opened, the intake check valve is closed, andthe drive unit exerts pressure P₂ on the system, which forces the bottompiston A₂ down with force F₂. Top piston A₁ moves up exerting force F₁,and pressure P₁ is exerted upwards on the product water tank. FIG. 31 isa block diagram depicting the recharge stroke Hygr Fluid System. Thetransfer check valve is closed, the intake check valve is opened, andpressure P₂ is exerted from the bottom piston A₂ to the drive unit andthe top piston A₁. Top piston A₁ moves up exerting force F₁, andpressure P₁ is exerted downwards from the product water tank. The powerand recharge strokes alternate, providing pumping action.

The present application discloses a pump having increased energyefficiency. The pumps disclosed reduce maintenance costs by reducing thenumber of moving parts and/or reducing the damage caused by suspendedparticles. In many pumping applications, a motor must be placed downholeto pump the fluid to the surface and such motors often require adownhole cooling system. One advantage of some embodiments disclosedherein is the elimination of the requirement of a downhole coolingsystem.

Methods and devices suitable for use in conjunction with aspects of thepreferred embodiments are disclosed in U.S. Pat. No. 6,193,476 and U.S.Pat. No. 7,967,578, both of which are hereby incorporated by referencein their entireties.

Methods and devices suitable for use in conjunction with aspects of thepreferred embodiments are disclosed in U.S. Patent Publication No.2008-0219869-A1; U.S. Patent Publication No. 2005-0169776-A1; and U.S.Patent Publication No. 2011-0255997-A1, which are also herebyincorporated by reference in their entireties.

The above description presents the best mode contemplated for carryingout the present invention, and of the manner and process of making andusing it, in such full, clear, concise, and exact terms as to enable anyperson skilled in the art to which it pertains to make and use thisinvention. This invention is, however, susceptible to modifications andalternate constructions from that discussed above that are fullyequivalent. Consequently, this invention is not limited to theparticular embodiments disclosed. On the contrary, this invention coversall modifications and alternate constructions coming within the spiritand scope of the invention as generally expressed by the followingclaims, which particularly point out and distinctly claim the subjectmatter of the invention. While the disclosure has been illustrated anddescribed in detail in the drawings and foregoing description, suchillustration and description are to be considered illustrative orexemplary and not restrictive.

All references cited herein are incorporated herein by reference intheir entireties. To the extent publications and patents or patentapplications incorporated by reference contradict the disclosurecontained in the specification, the specification is intended tosupersede and/or take precedence over any such contradictory material.

Unless otherwise defined, all terms (including technical and scientificterms) are to be given their ordinary and customary meaning to a personof ordinary skill in the art, and are not to be limited to a special orcustomized meaning unless expressly so defined herein. It should benoted that the use of particular terminology when describing certainfeatures or aspects of the disclosure should not be taken to imply thatthe terminology is being re-defined herein to be restricted to includeany specific characteristics of the features or aspects of thedisclosure with which that terminology is associated. Terms and phrasesused in this application, and variations thereof, especially in theappended claims, unless otherwise expressly stated, should be construedas open ended as opposed to limiting. As examples of the foregoing, theterm ‘including’ should be read to mean ‘including, without limitation,’‘including but not limited to,’ or the like; the term ‘comprising’ asused herein is synonymous with ‘including,’ ‘containing,’ or‘characterized by,’ and is inclusive or open-ended and does not excludeadditional, unrecited elements or method steps; the term ‘having’ shouldbe interpreted as ‘having at least;’ the term ‘includes’ should beinterpreted as ‘includes but is not limited to;’ the term ‘example’ isused to provide exemplary instances of the item in discussion, not anexhaustive or limiting list thereof; adjectives such as ‘known’,‘normal’, ‘standard’, and terms of similar meaning should not beconstrued as limiting the item described to a given time period or to anitem available as of a given time, but instead should be read toencompass known, normal, or standard technologies that may be availableor known now or at any time in the future; and use of terms like‘preferably,’ ‘preferred,’ ‘desired,’ or ‘desirable,’ and words ofsimilar meaning should not be understood as implying that certainfeatures are critical, essential, or even important to the structure orfunction of the invention, but instead as merely intended to highlightalternative or additional features that may or may not be utilized in aparticular embodiment of the invention. Likewise, a group of itemslinked with the conjunction ‘and’ should not be read as requiring thateach and every one of those items be present in the grouping, but rathershould be read as ‘and/or’ unless expressly stated otherwise. Similarly,a group of items linked with the conjunction ‘or’ should not be read asrequiring mutual exclusivity among that group, but rather should be readas ‘and/or’ unless expressly stated otherwise.

Where a range of values is provided, it is understood that the upper andlower limit, and each intervening value between the upper and lowerlimit of the range is encompassed within the embodiments.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations may be expressly set forth herein for sakeof clarity. The indefinite article ‘a’ or ‘an’ does not exclude aplurality. A single processor or other unit may fulfill the functions ofseveral items recited in the claims. The mere fact that certain measuresare recited in mutually different dependent claims does not indicatethat a combination of these measures cannot be used to advantage. Anyreference signs in the claims should not be construed as limiting thescope.

It will be further understood by those within the art that if a specificnumber of an introduced claim recitation is intended, such an intentwill be explicitly recited in the claim, and in the absence of suchrecitation no such intent is present. For example, as an aid tounderstanding, the following appended claims may contain usage of theintroductory phrases ‘at least one’ and ‘one or more’ to introduce claimrecitations. However, the use of such phrases should not be construed toimply that the introduction of a claim recitation by the indefinitearticles ‘a’ or ‘an’ limits any particular claim containing suchintroduced claim recitation to embodiments containing only one suchrecitation, even when the same claim includes the introductory phrases‘one or more’ or ‘at least one’ and indefinite articles such as ‘a’ or‘an’ (e.g., ‘a’ and/or ‘an’ should typically be interpreted to mean ‘atleast one’ or ‘one or more’); the same holds true for the use ofdefinite articles used to introduce claim recitations. In addition, evenif a specific number of an introduced claim recitation is explicitlyrecited, those skilled in the art will recognize that such recitationshould typically be interpreted to mean at least the recited number(e.g., the bare recitation of ‘two recitations,’ without othermodifiers, typically means at least two recitations, or two or morerecitations). Furthermore, in those instances where a conventionanalogous to ‘at least one of A, B, and C, etc.’ is used, in generalsuch a construction is intended in the sense one having skill in the artwould understand the convention (e.g., ‘a system having at least one ofA, B, and C’ would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). In those instances where aconvention analogous to ‘at least one of A, B, or C, etc.’ is used, ingeneral such a construction is intended in the sense one having skill inthe art would understand the convention (e.g., ‘a system having at leastone of A, B, or C’ would include but not be limited to systems that haveA alone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase ‘A or B’ will be understood toinclude the possibilities of ‘A’ or ‘B’ or ‘A and B.’

All numbers expressing quantities of ingredients, reaction conditions,and so forth used in the specification are to be understood as beingmodified in all instances by the term ‘about.’ Accordingly, unlessindicated to the contrary, the numerical parameters set forth herein areapproximations that may vary depending upon the desired propertiessought to be obtained. At the very least, and not as an attempt to limitthe application of the doctrine of equivalents to the scope of anyclaims in any application claiming priority to the present application,each numerical parameter should be construed in light of the number ofsignificant digits and ordinary rounding approaches.

Furthermore, although the foregoing has been described in some detail byway of illustrations and examples for purposes of clarity andunderstanding, it is apparent to those skilled in the art that certainchanges and modifications may be practiced. Therefore, the descriptionand examples should not be construed as limiting the scope of theinvention to the specific embodiments and examples described herein, butrather to also cover all modification and alternatives coming with thetrue scope and spirit of the invention.

What is claimed is:
 1. A pumping apparatus, comprising: a first inlethaving an inlet valve; an outlet for product fluid, the outlet having apressure maintaining valve; an accumulator in fluid communication withthe pressure maintaining valve; an internal power fluid column, theinternal power fluid column having a second inlet; a transfer pistonreciprocatingly mounted about the power fluid column; a product fluidchamber positioned above the transfer piston; a transfer chamberpositioned below the transfer piston; a sealable channel in the transferpiston fluidly connecting the product fluid chamber and the transferchamber, the sealable channel having a transfer piston valve; and atleast one passageway fluidly connecting the power fluid column with apower fluid chamber.
 2. The pumping apparatus of claim 1, wherein theapparatus is configured to pressurize fluid inside the power fluidcolumn and the power fluid chamber.
 3. The pumping apparatus of claim 2,wherein the transfer piston is configured such that the fluid actsagainst a first area comprising at least a portion of the transferpiston in a direction of transfer piston movement.
 4. The pumpingapparatus of claim 3, wherein the first area is greater than a secondarea comprising at least a portion of the transfer piston in the powerfluid chamber, and wherein the transfer piston is configured such thatthe fluid in the power fluid chamber acts against the second area in adirection of movement of the transfer piston.
 5. The pumping apparatusof claim 1, further comprising a first valve stop configured to preventclosing of the inlet valve and a second valve stop configured to preventclosing of the transfer piston valve.
 6. The pumping apparatus of claim5, wherein at least one of the first valve stop and the second valvestop comprises an extended portion on the rod portion of the transferpiston or a v-shaped member configured to prevent the transfer pistonvalve from closing when the v-shaped member contacts an activator. 7.The pumping apparatus of claim 1, wherein the power fluid column isinternal and the power fluid chamber, the transfer chamber and theproduct chamber are situated coaxially about the power fluid column. 8.The pumping apparatus of claim 1, configured for use in a deep well,wherein the system is configured to operate using a power fluidcomprising water or a hydraulic fluid.
 9. The pumping apparatus of claim8, wherein at least one of the power fluid chamber and the power fluidcolumn comprises stainless steel or titanium.
 10. The pumping apparatusof claim 1, further comprising a solenoid valve configured to controloscillation of a high head, whereby oscillating pressure to the powerfluid is delivered.
 11. The pumping apparatus of claim 1, furthercomprising a fluid inlet screen configured to filter fluid entering thefirst inlet.
 12. The pumping apparatus of claim 1, further comprising acoaxial disconnect.
 13. The pumping apparatus of claim 1, furthercomprising a subterranean switch pump comprising a power hydraulic lineand a recovery hydraulic line.
 14. The pumping apparatus of claim 1,further comprising a power fluid within the power fluid column and powerfluid chamber.
 15. The pumping apparatus of claim 1, wherein theaccumulator is a transfer barrier accumulator configured to controltiming of pressure applied alternatingly on the power fluid column andon the product fluid column.
 16. The pumping apparatus of claim 1,further comprising a housing, wherein the first inlet, the outlet, andthe internal power fluid column are disposed within the housing, whereinthe transfer piston slidably and sealingly extends between the powerfluid column and an interior wall of the housing, and wherein theproduct fluid chamber and the transfer chamber are at least partiallydefined by the interior wall of the housing.
 17. The system of claim 16,further comprising a coaxial disconnecting device, wherein the coaxialdisconnecting device is separately sealed to the power fluid column andthe product fluid chamber, whereby fluid communication between the powerfluid column and the coaxial disconnecting device is provided, andwhereby fluid communication between the product fluid chamber and thecoaxial disconnecting device is provided.
 18. A method for pumping afluid, the method comprising: introducing a power fluid into the powerfluid chamber of a pumping apparatus of claim 1 via the internal powerfluid column, whereby the transfer piston is lifted so as to close thetransfer piston valve, whereby fluid to be pumped is drawn into thetransfer chamber via the inlet valve; decreasing a pressure of the powerfluid in the power fluid column and the power fluid chamber, whereby thetransfer piston falls, the transfer piston valve is opened, and theinlet valve is closed, whereby the fluid to be pumped passes from thetransfer chamber via the transfer piston valve into the product fluidchamber; and increasing the pressure of the power fluid in the powerfluid column and the power fluid chamber, whereby the transfer piston israised, and the transfer piston valve closes, such that fluid to bepumped in the product chamber is forced out of the product chamber, suchthat the power fluid is pumped, wherein the accumulator provides forceover that created by a head of the internal power fluid column.
 19. Themethod of claim 18, wherein the pressure of the power fluid is increasedand decreased through application of an oscillating pressure to thepower fluid by moving a piston back and forth in a cylinder containingthe power fluid, and wherein motion of the piston is induced byoperation of at least one device selected from the group consisting of amotor, an engine with a crank mechanism, a pneumatic device, and ahydraulic device.
 20. The method of claim 19, wherein providingoscillating pressure to the power fluid comprises providing a column ofpower fluid extending to an elevation higher than an elevation at whichproduct fluid is recovered, wherein introducing a power fluid into apower fluid chamber of a pumping apparatus via an internal power fluidcolumn comprises closing a valve to a power fluid source and opening apower fluid release valve at an elevation lower than an elevation atwhich the pumped fluid is recovered, whereby the power fluid isintroduced into the power fluid chamber.